Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: AP Statistics Unit 2 (2026-27) · Level: Grade 12 AP Statistics
Question 1 Two-Way Table (2 points)
A district surveyed 180 students about lunch.
| Hot lunch | Cold lunch | Total | |
|---|---|---|---|
| Middle school | 48 | 32 | 80 |
| High school | 36 | 64 | 100 |
| Total | 84 | 96 | 180 |
- Find P(high school and hot lunch) and P(cold lunch). (1 point)
- Find P(hot lunch | middle school). Are lunch choice and school level independent? Justify. (1 point)
Question 2 Venn Diagram Probabilities (2 points)
The Venn diagram shows probabilities for events A and B.
- Find P(A or B). (1 point)
- Find P(A | B). (1 point)
Question 3 Independent Events (2 points)
For events A and B, P(A) = 0.6, P(B) = 0.5 and P(A or B) = 0.8. Are A and B independent? Justify.
Question 4 Tree Diagram (3 points)
A student commutes by bike, bus or on foot with the probabilities shown.
- Find the probability that the student is late. (1 point)
- Given that the student is late, find the probability that the student took the bus. (1 point)
- Are lateness and commute method independent? Explain. (1 point)
Question 5 Simulation Design (2 points)
A basketball player makes 60% of her free throws. Describe a simulation using random digits to estimate the probability that she makes at least 3 of her next 4 shots, and state how the estimate is computed.
Question 6 Discrete Random Variable (3 points)
Let X be the number of siblings of a randomly chosen student: P(0) = 0.30, P(1) = k, P(2) = 0.20, P(3) = 0.10.
- Find k. (1 point)
- Find the mean of X. (1 point)
- Find the standard deviation of X. (1 point)
Question 7 Expected Value (2 points)
A game costs $2 to play. A fair die is rolled: a 6 wins $6, a 4 or 5 wins $2, and any other roll wins nothing. Find the expected net gain and interpret it.
Question 8 Without Replacement (2 points)
A bag holds 5 red chips and 7 blue chips. Two chips are drawn at random without replacement. Find the probability that (a) both are red, (b) the two chips have different colors.
Question 9 At Least One (2 points)
Three traffic lights on a route operate independently, and each is green when a driver arrives with probability 0.4. Find the probability that the driver meets at least one green light.
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