AP Statistics 2.7: Independent Events and Unions

Calculate probabilities for independent events and unions by checking independence and applying the multiplication and addition rules.

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.

Model Solution
Because any song can be replayed, the selections are independent:
$P(\text{both rock})=(0.10)(0.10)=0.01.$

Scoring components
3. Calculates the probability consistently with part A(i).
4. Shows supporting work consistent with part A(i).

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2.7.A—Calculate probabilities for independent events and for the union of two events question 1