Question

Use the following information to answer the next four exercises. Table 3.15 shows a random sample of musicians and how they learned to play their instruments.

Find P(musician is a female OR is self taught).

Short answer

$P(musicianisafemaleORisselftaught)=0.7$

Step-by-step solution

Content Introduction

The contingency table shown below:

Content Explanation

It can be seen in the table that total number of musicians is $130$,out of these total musicians, $72$are female musician and $31$musicians learned music by themselves. Therefore probability of musician is female or is self taught as follow:

$$\begin{gathered} P(musicianisafemaleORisselftaught)=P(femalemusician)+P(musicianselftaught)-P(musicianisfemaleandselftaught) \\ P(musicianisafemaleORisselftaught)=\frac{72}{130}+\frac{31}{130}-\frac{12}{130} \\ P(musicianisafemaleORisselftaught)=0.7 \end{gathered}$$