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

Step-by-step 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.