AP Statistics Conditional Probability and Independence Test with Point Values (PDF)

AP Statistics math test: Conditional Probability and Independence – Maths PDF

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This conditional probability test for AP Statistics covers conditional probability and independence (Common Core AP STAT 4.5, AP STAT 4.6, HSS-CP.A.2, HSS-CP.A.3, HSS-CP.A.4, HSS-CP.B.6, HSS-CP.B.8), with a free PDF to print.

This 45-minute test covers conditional probability, the multiplication rule, tree diagrams, and independence. Show the formula or table row you use and give each answer as a fraction or decimal.

Time and points

About this test

Grade: AP Statistics
Chapter: Conditional Probability and Independence
Standards: AP STAT 4.5, AP STAT 4.6, HSS-CP.A.2, HSS-CP.A.3, HSS-CP.A.4, HSS-CP.B.6, HSS-CP.B.8
Time: 45 minutes
Total: 20 points

Conditional probability test: questions

Question 1 – Conditional from a table [3 pts]

Opinion by sex.

(a) Find P(likes | girl). (1 point) (b) Find P(girl | likes). (1 point) (c) Are liking and sex independent? (1 point)

Question 2 – Tree diagram [4 pts]

A tree for bus arrival.

(a) Find P(rain and late). (1 point) (b) Find P(late). (1 point) (c) Find P(rain | late). (2 points)

Question 3 – Independence [3 pts]

P(A) = 0.5, P(B) = 0.2, and P(A or B) = 0.6. (a) Find P(A and B). (1 point) (b) Are A and B independent? (1 point) (c) Are they mutually exclusive? (1 point)

Question 4 – Without replacement [2 pts]

A drawer has 5 black and 3 white socks. Two are chosen at random without replacement. Find P(both black).

Question 5 – At least one [2 pts]

A basketball player makes 75% of free throws, independently. Find the probability that she makes at least one of two shots.

Question 6 – Explain the difference [2 pts]

Explain the difference between independent events and mutually exclusive events using the roll of one die: A = even number and B = a 6.

Question 7 – Medical test [3 pts]

A condition affects 5% of people. A test is positive for 90% of people with the condition and 8% of people without it. Find P(positive) and P(condition | positive). (3 points)

Question 8 – Read the notation [1 pt]

Independence check.

Write P(rain | late) in words.

Key facts behind this conditional probability test

Key facts

P(A | B) = P(A and B) / P(B): restrict to the outcomes where B occurred.
General multiplication rule: P(A and B) = P(B) P(A | B).
Independent: P(A | B) = P(A), so P(A and B) = P(A) P(B).
Mutually exclusive events with positive probabilities are never independent.
Tree diagrams multiply along branches and add the paths that fit the event.

How to use this conditional probability test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

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