Question

The table 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?

Short answer

The event "being a female musician" and "learning music in school" are not mutually exclusive.

Step-by-step solution

Given information

The given table shows a random sample of musicians and how they learned to play their instruments.

Calculation

Now solving,

$$\begin{gathered} P\left(\text{Musician is a female}\right)=\frac{\text{No. of favorable event}}{\text{Total no. of events}} \\ P\left(\text{Beingafemalemusicianandlearningmusicinschool}\right)=\frac{38}{130} \\ =0.2923 \end{gathered}$$

There are total $130$musicians and out of which $72$females and $58$males and there are $38$female musicians who is studied in school.

Since the probability of "being a female musician" and "learning music in school" is not equal to 0. So, these two events are not mutually exclusive.

For two events like A and B are mutually exclusive, then Probability (A and B) must be equal to 0.

There should be nothing in common between these two events.

But in our question, it is not equal to zero.

Final answer

No, the event "being a female musician" and "learning music in school" are not mutually exclusive.