AP Statistics 2.10: Binomial Probabilities

Calculate binomial probabilities for exact, cumulative, or at-least outcomes by defining the success count and using n, p, and the relevant event.

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.

Recall that in every one-hour period, 20 songs will be played at random and any song can be

replayed at any time.

Determine the probability that 4 or more rock songs in a particular one-hour period will

be played. Show your work.

Model Solution
$\begin{aligned} P(X\ge4)&=1-P(X\le3)\\ &=1-\sum_{x=0}^{3}\binom{20}{x}(0.10)^x(0.90)^{20-x}\\ &=1-0.867=0.133. \end{aligned}$

Scoring components
1. Gives the correct probability.
2. Shows work supporting the probability.

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2.10.E—Calculate probabilities for a binomial distribution question 1