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.

Are the events “being a female musician” and “learning music in school” mutually exclusive events?

The contingency table is shown below:

To see event “being a female musician” and “learning music in school” are mutually exclusive events or not, consider the probability of event being a female musician AND learning music in school.

If the probability of the event being a female musician and learning music in school is equal to zero, then it will be concluded both events are mutually exclusive.

It can be seen that total number of musicians is$130$and $38$are female musician who learned music in school. To calculate

$$\begin{gathered} P(beingafemalemusicianandlearningmusicinschool)=\frac{femalmusicianwholearnedmusicinschool}{totalmusicians} \\ P(beingafemalemusicianandlearningmusicinschool)=\frac{38}{130} \\ P(beingafemalemusicianandlearningmusicinschool=0.29 \end{gathered}$$

Hence, the probability being a female musician and learning music in school is not equal to zero.