HSS.CP.A.5Common CoreMathStatistics and ProbabilityGrades 9-12
HSS.CP.A.5: Conditional Probability and Independence in Everyday Language
In plain English: HSS.CP.A.5 is the Common Core statistics and probability standard that asks students to recognize and explain conditional probability and independence in everyday situations. Students turn phrases such as "given that" or "of those who" into P(A | B), tell P(A | B) apart from P(B | A), and judge whether knowing one event changes the chance of another. It is usually taught in Geometry or Algebra II.
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
Common Core State Standards for Mathematics · Domain: Conditional Probability and the Rules of Probability (CP) · Cluster: Understand independence and conditional probability and use them to interpret data Also written as HSS-CP.A.5 or S-CP.5 · Official standard
This lesson is about meaning rather than heavy computation. Students learn to hear a conditional probability in ordinary speech ("if", "given that", "among", "of those who") and to name the condition: the group that the probability is restricted to. They practice the difference between a statement and its reversal, which is the idea behind the official example comparing the chance of lung cancer for smokers with the chance of being a smoker for people who have lung cancer.
Students then explain independence in plain words: two events are independent when knowing that one happened does not change the chance of the other. They test the idea on coins, raffles, weather and shopping, separate independence from "cannot happen together", and use small invented data sets to support their explanations with numbers.
Learning Objectives
By the end of this lesson, students will be able to:
Recognize a conditional probability in everyday language and write it as P(A | B), naming the condition
Explain why P(A | B) and P(B | A) answer different questions, using the official smoking and lung cancer example
Explain independence in everyday words as "knowing one event does not change the chance of the other"
Decide whether events in everyday situations are likely independent or dependent, and justify the decision with a reason or with data
Prior Knowledge Required
Students should already be comfortable with:
Probability as a number from 0 to 1 that describes likelihood 7.SP.C.5
Finding probabilities as fractions of equally likely outcomes 7.SP.C.7
Reading two-way tables and finding a proportion of a row or column 8.SP.A.4
Describing events as subsets of a sample space HSS.CP.A.1
Write two sentences on the board and ask students to vote on each: true or false?
Warm-Up Prompt
"Sentence 1: Almost every professional basketball player is taller than average. Sentence 2: Almost every person who is taller than average is a professional basketball player. They use the same words. Why is one true and the other false?"
Students quickly agree that the first is true and the second is false. Ask them to say which group each sentence is talking about: the first looks only at basketball players, the second looks at all tall people, a huge group in which basketball players are a tiny part. Name the idea: each sentence is a conditional probability, and swapping the condition changes the question.
Direct Instruction20-25 minutes
Part 1: Hearing a conditional probability. Everyday speech signals a condition with words such as if, given that, when, among, of those who and out of. The condition is the group we already know we are in. Write it after the bar: P(A | B) is read "the probability of A given B".
Translating a sentence
"Among students who play a varsity sport, 30% have a part-time job."
Equation: P(job | varsity) = 0.30. The condition is "plays a varsity sport"; the sentence says nothing about P(varsity | job).
Official example: smoker and lung cancer
Invented round numbers, not medical data: in a group of 10,000 adults, 1,500 smoke, 100 have lung cancer, and 80 of the 100 are smokers.
Equation: P(lung cancer | smoker) = 80/1,500 ≈ 0.053, while P(smoker | lung cancer) = 80/100 = 0.80
Independence: a coin streak
A fair coin has landed heads five times in a row. Is tails "due" on the next flip?
Equation: P(tails on flip 6 | heads on flips 1-5) = 1/2 = P(tails): the coin has no memory, so the flips are independent.
Dependence: drawing without replacement
A jar holds 10 raffle tickets, and 3 are winners. Two tickets are drawn, one after the other, and the first is not put back.
Equation: P(2nd wins | 1st wins) = 2/9 ≈ 0.22, but P(2nd wins) = 3/10, so the two draws are dependent.
Part 2: The official example. Work Example 2 with Diagram 1. Both probabilities share the same 80 people, but the "out of" group changes. The smokers are a large group, and only a small part of it has lung cancer; the lung cancer patients are a small group, and most of it smokes. In everyday words: "Most people with lung cancer in this group smoke" is a very different statement from "most smokers get lung cancer", and only the first one is true for these numbers. Emphasize that the numbers are invented to show the idea; students should not quote them as facts.
Part 3: Independence in everyday words. Two events are independent when knowing that one happened does not change the probability of the other. Use Examples 3 and 4 and Diagram 2, then give students a test sentence to use: "Knowing ___ happened changes / does not change the chance that ___."
Name the two events in plain words.
Ask the knowing question: if I learned the first event happened, would I change my estimate for the second?
Look for a mechanism: a physical connection (the ticket is gone, the weather affects sales) points to dependence; separate processes (two flips of a fair coin) point to independence.
Check with data when you can: compare the proportion for the second event with and without the first event.
Close with a common confusion. Events that cannot happen together, such as "the traffic light is red" and "the same light is green" at one moment, are not independent: knowing one happened makes the other impossible, so its chance drops to 0.
Guided Practice15 minutes
Project these statements one at a time. Pairs write each as P(A | B), name the condition, and then say the reversed statement aloud.
"If it is a school day, the chance that Jordan's alarm rings at 6:30 is 0.95." (P(alarm at 6:30 | school day); condition: school day.)
"Among dogs at the shelter, 40% are puppies." (P(puppy | shelter dog).)
"Of the people who ordered dessert, 70% also ordered coffee." (P(coffee | dessert). The reversal, P(dessert | coffee), could be very different.)
"A package shipped express arrives the next day 9 times out of 10." (P(next day | express).)
Then ask for a judgment on two pairs: "My bus is late" and "I ate cereal for breakfast" (independent: breakfast cannot affect the bus); "It snowed overnight" and "school starts late" (dependent: snow makes a delayed start more likely).
Independent Practice15 minutes
Students work alone:
Write two everyday sentences that state a conditional probability, then write each reversal and explain whether it means the same thing.
Give one pair of events that you expect to be independent and one pair you expect to be dependent. Use the sentence "Knowing ___ changes / does not change the chance that ___."
A shoe store (invented data) had 200 customers who bought running shoes, and 50 of them also bought socks; of 300 customers who bought other shoes, 45 bought socks. Find the chance of buying socks for each group and explain in words whether buying socks is independent of buying running shoes. (0.25 versus 0.15: dependent. Knowing a customer bought running shoes raises the chance of a sock purchase.)
Closure5 minutes
Exit ticket: (1) In one sentence, explain the difference between "the chance that a person owns a guitar, given that they play in a band" and "the chance that a person plays in a band, given that they own a guitar". (The first looks only at band members; the second looks at all guitar owners, a larger group that includes many people not in a band.) (2) Give one pair of independent events from your own life and explain why.
Differentiation Strategies
For Struggling Students
Give a sentence frame for every conditional statement: "Out of all ___, the chance of ___ is ___"
Have students underline the condition in each sentence before writing any notation
Use small groups of real objects (for example, 10 counters in two colors, some marked with a dot) so students can physically set aside the condition group
For Advanced Students
Ask students to invent counts for a group of 1,000 people in which P(A | B) is 0.9 but P(B | A) is only 0.1, and to explain what makes the gap so large
Have students find a claim in a newspaper or advertisement that uses a conditional probability and explain which way the condition goes
Ask students to explain why independence of A and B means that P(B | A) = P(B) as well, using a two-way table with totals
Assessment Guidance
What to Look For
Listen for students who can name the condition in their own words ("out of the smokers" or "only the people with lung cancer"), not only point to the symbol after the bar. A strong explanation of independence uses the knowing test and gives a reason or a comparison of proportions; a weak one says "they are unrelated" with no reason. Watch for two confusions: treating a statement and its reversal as the same, and calling events independent because they cannot happen together.
02
Classroom Activities
3 Activities
1
Which Way Is the Condition?
20 minGroups of 3-4
Groups match 12 statement cards into 6 reversed pairs, name the condition on each card, and decide which probability in each pair is larger. This is the reasoning of the official smoking and lung cancer example applied to everyday situations.
Card Pairs
P(has four legs | is a dog) and P(is a dog | has four legs)
P(speaks Spanish | lives in Madrid) and P(lives in Madrid | speaks Spanish)
P(the ground is wet | it rained overnight) and P(it rained overnight | the ground is wet)
P(owns a winter coat | lives in Minnesota) and P(lives in Minnesota | owns a winter coat)
P(can cook pasta | is a professional chef) and P(is a professional chef | can cook pasta)
P(wears a cast | has a broken arm) and P(has a broken arm | wears a cast)
Procedure
Groups shuffle the cards, find the 6 pairs, and write the condition of each card in words ("out of all dogs")
For each pair, groups decide which probability is larger and write one sentence explaining why, using the sizes of the two condition groups
Groups present one pair where they disagreed at first
Discussion Questions
In which pairs are both probabilities fairly high? What makes the two groups similar in size?
How is the Madrid pair like the smoking and lung cancer example?
2
Coin Streak Experiment
20 minPairs
Pairs test whether a coin "remembers" a streak. They collect real flips, look only at the flips that come right after three heads in a row, and compare the proportion of heads there with the proportion of heads overall.
Procedure
Each pair flips a coin 100 times (or uses a random number generator) and records the results as a string of H and T
Pairs circle every flip that comes right after three heads in a row and count how many of those circled flips are heads
Pairs compute two proportions: heads among the circled flips, and heads among all 100 flips
The class pools its circled flips on the board, since each pair has only a few
Discussion Questions
Were the two proportions close? Why might one pair's circled proportion be far from 1/2 even if the coin has no memory?
Say the result as an independence sentence: "Knowing the last three flips were heads ___ the chance of heads."
Name a situation where people act as if a streak changes the chances. Is that reasonable there?
Modification for Distance Learning
Students use a spreadsheet random function to generate 1,000 flips and a formula to flag flips that follow three heads, then share the two proportions in a class form.
3
Independent or Dependent? Scenario Debate
20 minGroups of 3-4
Groups decide whether the two events on each of 8 scenario cards are independent or dependent, explain in everyday words, and describe what data could check their answer.
Scenario Cards
A die shows 4, and a coin tossed at the same time shows heads (independent)
Two cards drawn without replacement: the first is a heart, the second is a heart (dependent)
Two cards drawn with the first put back and the deck shuffled: both hearts (independent)
It is a cold, rainy day, and a cafe sells more hot chocolate (dependent)
A randomly chosen person was born in May, and the person has brown eyes (reasonable to treat as independent)
A student studies for a test, and the student passes (dependent)
Two strangers in different cities each get a flat tire today (reasonable to treat as independent)
A family's first child and second child both have red hair (dependent: children share parents)
Procedure
Each group member takes two cards and writes a "knowing ... changes / does not change ..." sentence for each
The group discusses each card and records a final decision and one piece of data that could test it
Groups post their decisions, and the class discusses any card with split votes
Challenge Variation
Groups write a new card that seems independent at first but turns out to be dependent, and explain the hidden connection.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: The Official Example, Two Different Groups
Drawn to scale with invented round numbers. The shaded part of each bar is the same 80 people. Out of the 1,500 smokers, those 80 are a thin slice; out of the 100 people with lung cancer, they are most of the bar. Changing the condition changes the question and the answer.
Diagram 2: The Knowing Test for Independence
Bars drawn to scale on a 0 to 1 axis. For a fair coin, learning about earlier flips leaves the chance of tails at 1/2, so the flips are independent. In the raffle, learning that the first ticket won leaves fewer winners in the jar, so the chance for the second draw drops from 3/10 to 2/9: the draws are dependent.
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Homework Assignment
~30 min
HSS.CP.A.5 Homework: Conditional Probability and Independence in Words
Directions: Answer in complete sentences. For every conditional probability, name the condition in words ("out of all ..."). For every independence question, use a sentence of the form "Knowing ___ changes / does not change the chance that ___". All numbers are invented for practice.
Part 1: Conditional Probability in Everyday Language (Problems 1-3)
Write each statement as P(A | B) and name the condition in words. (a) "Of the customers who order a large coffee, 40% also buy a pastry." (b) "If a flight leaves late, the chance it still arrives on time is 0.25." (c) "Only 1 in 8 of the raffle tickets sold at the door were winners." (d) "Knowing that a movie is a sequel, there is a 30% chance critics rate it above 80."
A school newsletter says: "Most students who earned an A in chemistry attended the optional review session." A parent concludes: "So most students who attend the review session earn an A." Explain the parent's error in conditional probability language. Then invent counts for a class of 40 students in which the newsletter's statement is true but the parent's is false, and compute both probabilities.
In a coastal region (invented data), a beach town has 2,000 residents and 300 of them own a surfboard; the inland towns have 18,000 residents and 100 of them own a surfboard. Compare the chance that a resident owns a surfboard if they live in the beach town with the chance that a resident lives in the beach town if they own a surfboard. Compute both and explain in everyday words why they are so different.
Part 2: Independence in Everyday Situations (Problems 4-6)
Decide whether each pair of events is likely independent or dependent, and explain with a knowing sentence. (a) A spinner lands on blue, and on a second spin it lands on blue again. (b) The power goes out in a neighborhood, and the food in its refrigerators warms up. (c) Two different students are chosen from a class of 25 for two jobs, and both are juniors. (d) A randomly chosen adult is left-handed and was born on a Tuesday.
A bus route made 200 trips last month (invented data). On the 40 trips in rain, the bus was late 12 times; on the 160 dry trips, it was late 16 times. (a) Find P(late | rain), P(late | dry) and P(late). (b) Explain in everyday words whether "late" and "rain" are independent. (c) Find P(rain | late) and say in words what it means.
A friend always avoids last week's winning numbers when buying a lottery ticket, "because those numbers just came up." Explain, using the idea of independence, why this strategy does not change the chance of winning (assume each weekly drawing is random and separate). Then give your own example of two dependent events from daily life and explain what connects them.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Condition Named
The condition is named correctly in words for every conditional probability
One condition reversed or missing
Conditions not named
Reversal Explained
Explains clearly why P(A | B) and P(B | A) differ, with group sizes
States that they differ without a reason
Treats them as the same
Independence Reasoning
Every decision uses the knowing test with a reason or data
Decisions correct, reasons thin
Decisions wrong or unexplained
Accuracy
All computed probabilities correct
One computation wrong
Several errors
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Choose or write an answer for each question, then open the explanation. Numbers in the questions are invented. Your score updates as you go, and Reset quiz clears the quiz for another try.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which sentence describes P(sunburn | beach day)?
Answer: B
The event after the bar, beach day, is the condition, so we look only at beach days and ask how often a sunburn happens. Choice A reverses the condition. Choice C describes a joint probability, "and", with no restriction.
Question 2 of 20 · Multiple Choice
"Of the students in the chess club, 25% are also on the math team." Which notation matches this sentence?
Answer: D
"Of the students in the chess club" names the group we restrict to, so chess club is the condition. Choice A reverses it: it would describe the share of math team members who play chess. Choice B would be a share of all students, not of the chess club.
Question 3 of 20 · Multiple Choice
"The probability that a customer returns a jacket, if the jacket was bought online, is 0.18." What is the condition?
Answer: A
The word "if" introduces the condition: we look only at jackets bought online. Choice B is the event whose chance is being given, and choice D misreads the sentence as a joint probability.
Question 4 of 20 · Multiple Choice
Which pair of events is most reasonable to treat as independent?
Answer: C
Separate rolls of a fair die do not affect each other, so knowing today's roll does not change tomorrow's chances. In choice D the first ace leaves fewer aces in the deck, so the second draw depends on the first. Choices A and B have an obvious connection.
Question 5 of 20 · Multiple Choice
A fair six-sided die has landed on 6 three times in a row. What is the probability that the next roll is a 6?
Answer: C
Rolls of a fair die are independent, so the earlier rolls do not change the chance: it stays 1/6. Choice A is the gambler's fallacy. Choice D treats two outcomes as equally likely when they are not: "not a 6" covers five of the six faces.
Question 6 of 20 · Multiple Choice
A summer camp has 240 campers. 60 signed up for swimming, 45 signed up for archery, and 18 signed up for both. What is the probability that a camper who signed up for swimming also signed up for archery?
Answer: D
Given swimming, the group is the 60 swimmers, and 18 of them chose archery: 18/60 = 0.30. Choice A divides by all 240 campers, choice B is the share of campers who swim (60/240), and choice C reverses the condition (18/45 is the share of archers who swim).
Question 7 of 20 · Multiple Choice
In everyday language, what does it mean that events A and B are independent?
Answer: B
Independence is about information: learning B tells you nothing new about the chance of A. Choice A describes events that cannot happen together, which are dependent, and choice D confuses independence with equal probabilities.
Question 8 of 20 · Multiple Choice
Two events each have a positive probability but cannot happen at the same time. Are they independent?
Answer: D
If one event happens, the chance of the other drops to 0, so knowing one changes the chance of the other: the events are dependent. Choice A mixes up "no outcomes in common" with "independent".
Question 9 of 20 · Multiple Choice
A report (invented) says 90% of people with a certain pollen allergy sneeze often in spring. A student concludes that 90% of people who sneeze often in spring have the allergy. What is wrong?
Answer: A
The report restricts to people with the allergy; the student restricts to people who sneeze, a group that also includes people with colds and other allergies. Choice C just takes the complement, which answers a third question.
Question 10 of 20 · Multiple Choice
A bag holds 5 red and 3 blue marbles. You draw one marble, keep it, and draw another. What is P(second is red | first is red)?
Answer: B
After a red marble is removed, 4 of the 7 remaining marbles are red, so the chance is 4/7. Choice A ignores that the first marble was kept, and choice C removes a marble from the total but not from the red count.
Question 11 of 20 · Multiple Choice
In the marble situation above, which change would make the two draws independent?
Answer: C
With replacement, the bag is the same for both draws, so the first result cannot change the chances for the second. Choice A is the same as drawing without replacement, and choice D does not change what is left in the bag.
Question 12 of 20 · Multiple Choice
Which statement uses the word "independent" correctly?
Answer: A
The coin statement uses the knowing test correctly. Choice B describes a connection, which is dependence. Choice C describes events that cannot happen together, which are dependent, and choice D confuses units with independence.
Question 13 of 20 · Multiple Choice
A survey (invented data) finds that 35 of 50 dog owners walk every day and 20 of 50 people without a dog walk every day. Which conclusion fits?
Answer: B
Compare proportions: 35/50 = 0.70 for dog owners and 20/50 = 0.40 for non-owners, so knowing someone owns a dog changes the chance they walk daily. Choice A confuses equal group sizes with independence, and choice C claims a cause the survey cannot show.
Question 14 of 20 · Short Answer
A traffic app reports P(arrive on time | leave before 7:30) = 0.9. Write this in an everyday sentence. Then write the reversed probability in words and explain why it is a different question.
Sample answer: "If you leave before 7:30, there is a 90% chance you arrive on time," or "Of the trips that leave before 7:30, 90% arrive on time." The reversal is P(leave before 7:30 | arrive on time): "of the trips that arrive on time, what fraction left before 7:30?" It looks at a different group, on-time trips, which includes trips that left later.
Question 15 of 20 · Short Answer
Compare "the chance that a person owns a telescope if they are in the astronomy club" with "the chance that a person is in the astronomy club if they own a telescope". Explain in everyday language which is likely larger and why.
The first is likely much larger. In the first, the group is club members, a small group of people who are very interested in the sky, so many own telescopes. In the second, the group is all telescope owners, a larger group that includes many people who never joined a club. Both use the same overlap (club members who own telescopes) but divide it by groups of very different sizes.
Question 16 of 20 · Short Answer
A cafeteria (invented data) sold 400 lunches on pizza days this month, and 120 came with milk. On other days it sold 500 lunches, and 150 came with milk. Is buying milk independent of pizza day? Explain in everyday words and with numbers.
P(milk | pizza day) = 120/400 = 0.30 and P(milk | other day) = 150/500 = 0.30, which also equals P(milk) = 270/900 = 0.30. Yes, it appears independent: knowing that it is pizza day does not change the chance that a lunch comes with milk.
Question 17 of 20 · Short Answer
At a concert (invented data), 1,200 people attended, 700 were under 25, and 300 bought a T-shirt. Of the T-shirt buyers, 240 were under 25. Find P(T-shirt | under 25) and P(under 25 | T-shirt), and say in words what each one means.
P(T-shirt | under 25) = 240/700 ≈ 0.34: about a third of the attendees under 25 bought a T-shirt. P(under 25 | T-shirt) = 240/300 = 0.80: 80% of the T-shirt buyers were under 25. The overlap is the same 240 people, but the groups are different.
Question 18 of 20 · Short Answer
Give an everyday example of two events that are dependent, and explain the dependence with a sentence of the form "Knowing ___ changes the chance that ___".
Sample answer: "A store runs a half-price sale" and "the store is crowded". Knowing that the store is running a big sale changes the chance that it is crowded, because the sale draws extra shoppers. Any answer with a clear connection and a correct knowing sentence earns credit.
Question 19 of 20 · Short Answer
At a high school, the chance that a randomly chosen student is a senior is 0.25, while the chance that a student who drives to school is a senior is 0.60. A classmate says this shows that being a senior and driving to school are independent. Is the classmate right? Explain.
No. P(senior | drives) = 0.60 is very different from P(senior) = 0.25, so knowing that a student drives raises the chance that the student is a senior. That is dependence. It makes sense in everyday terms: seniors are older and more likely to have a license and a car.
Question 20 of 20 · Short Answer
A doctor says: "If a patient tests positive, the chance that they have the condition is about 50%." The patient replies: "But the test catches 95% of people who have the condition." Explain, using conditional probability language, how both statements can be true.
They are different conditional probabilities. The 95% is P(positive | has the condition): out of people who have it, the share who test positive. The 50% is P(has the condition | positive): out of people who test positive, the share who have it. If the condition is rare, many positive tests come from the much larger group of healthy people, so the second probability can be far lower than the first.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSS.CP.A.5 mean?
HSS.CP.A.5 means students can recognize conditional probability and independence in ordinary situations and explain them in plain words. It is less about calculating and more about reading a sentence like "of the people who ..." and knowing which group the probability is about, and about deciding whether one event gives information about another.
What is conditional probability in simple words?
It is the chance of something happening when you already know something else is true. You shrink the group you are looking at to the ones where the known fact holds, then ask how often the event happens inside that smaller group. "The chance a flight is full, given that it is the Friday evening flight" only looks at Friday evening flights.
What does independent mean in probability?
Independent means that learning one event happened gives no information about the other: the chance of the second event stays the same. Two spins of a fair spinner are independent. A useful test sentence is "Knowing ___ does not change the chance that ___."
Why is the chance of lung cancer for smokers different from the chance of smoking for lung cancer patients?
Because the two probabilities divide the same overlap by different groups. Smokers are a large group, and only part of it develops lung cancer; people with lung cancer are a much smaller group, and a large part of it smokes. That is the point of the official example: swapping the condition changes the question. The lesson uses invented round numbers so students see the idea without quoting medical statistics.
Is independent the same as mutually exclusive?
No, and the two are close to opposites. Mutually exclusive events cannot happen together, so if one happens the other has a chance of 0: knowing one changes the other, which makes them dependent (when both have positive probability). Independent events can happen together, and one does not affect the chance of the other.
What words signal a conditional probability?
Look for given that, if, when, among, of those who, out of and for people who. The phrase that follows names the condition, the group being restricted to. Ask students to rewrite the sentence as "Out of all ___, the chance of ___" to check.
What is the gambler's fallacy?
It is the belief that a streak changes the chances of independent events, such as thinking a coin is "due" for tails after several heads. For a fair coin, each flip is independent, so the chance of tails stays 1/2 no matter what came before. Activity 2 lets students test this with real flips.
Is HSS.CP.A.5 taught in Geometry or Algebra 2?
It varies by school. The Common Core model course pathways place the conditional probability standards in Geometry (traditional pathway) or Mathematics II (integrated pathway), and many schools teach them in Algebra II or a statistics course. It is usually taught right after or together with two-way tables (HSS.CP.A.4).
How is HSS.CP.A.5 assessed?
Typical tasks ask students to match a sentence to the right probability notation, spot a reversed condition, decide whether events in a scenario are independent and explain why, or compute a simple conditional probability from a description and say what it means. Written explanations matter as much as numbers for this standard.
How does HSS.CP.A.5 connect to HSS.CP.A.3 and HSS.CP.A.4?
HSS.CP.A.3 gives the formal definition, P(A | B) = P(A and B)/P(B), and states independence as P(A | B) = P(A). HSS.CP.A.4 uses two-way tables of data to estimate these probabilities. HSS.CP.A.5 asks students to explain the same ideas in everyday language, so it ties the formulas and tables to situations students recognize.
07
Related Standards
5 standards
These standards connect to HSS.CP.A.5: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
7.SP.C.5Prerequisite
Understand probability as a number from 0 to 1 that measures likelihood
