Question

In a class of 50 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose to raise his or her hand. Seven hands go up. Then the professor asked everyone with a pierced ear to do likewise. This time there are 46 hands raised. How many students have piercings both on their ears and their noses?

Answer 1

Answer: 3

Explanation:

Let E be the event of that student pierces ear and N be the event of that student pierces nose.

Given:
`n(E\cup N=50)`

`n(E)=46\\\\n(N)=7`

For any two event A and B, we have

`n(A\cup B)=n(A)+n(B)-n(A\cap B)`

Similarly ,
`n(E\cup N)=n(E)+n(N)-n(E\cap N)`

`50=46+7-n(E\cap N)\\\\\Rightarrow\ n(E\cap N)=53-50=3`

Hence, 3 students have piercings both on their ears and their noses.