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AP Statistics 2.7 Independent Events and Unions of Events Questions

Practise recognising independent event structure and calculating intersections, complements, unions, and multi-path probabilities with the appropriate rules.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • determine whether events are independent from conditional probabilities or the intersection product
  • calculate repeated independent-event probabilities directly or through an at-least-one complement
  • use the addition rule to calculate a union or recover an overlap from known event probabilities
  • combine mutually exclusive paths or outcome arrangements to obtain a complete event probability

Covered syllabus points

2.7.A—Calculate probabilities for independent events and for the union of two events

Question 1

Ms. Fey is a manager at a restaurant. To improve the dining experience for her customers, she uses a digital music service to create a playlist of songs that will be played in the restaurant.

The playlist contains 1,000 songs and consists of four different types of music in the following quantities: 200 country songs, 400 pop songs, 100 rock songs, and 300 jazz songs. The digital music service will select songs at random from the playlist to be played in the restaurant. Any song can be replayed at any time.

A.

Suppose two songs are selected at random to be played. What is the probability that both songs are rock songs? Show your work.

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