Question

Neil has 161 songs on a playlist. He categorized them in the following manner: 18 country, 27 rock, 21 rap, 32 jazz, 8 gospel, 14 latin American and 41 classical. if Neil begins listening to his playlist on shuffle, what is the probability that the first song played is a rock song? express your answer in a fraction

Answer 1

Answer

The probability that the first song to play is

$P(\text{rock songs)}=\frac{27}{161}$

SOLUTION

Problem Statement

The question says Neil has 161 songs on a playlist with 18 country, 27 rock, 21 rap, 32 jazz, 8 gospel, 14 latin American, and 41 classical.

We are asked to find the probability that if he puts his playlist on shuffle, that the first song played is a rock song.

Method

To solve the question, we need to know how to find the probability of an event occurring. This is given below:

$\begin{gathered} \text{Given an event (E) like playing a rock song in this question,} \\ P(E)=\frac{\text{Number of possibilities of Event (E)}}{\text{Number of possible occurrences}} \end{gathered}$

With this formula, we can easily solve the question.

Implementation

$\begin{gathered} \text{ Number of rock songs = 27} \\ \text{ Number of songs in the playlist = 161} \\ \\ \therefore P(\text{rock songs)}=\frac{27}{161} \end{gathered}$

Final Answer

The probability that the first song is a rock song is

$P(\text{rock songs)}=\frac{27}{161}$