Question

In a group of 27 pupils, 7 play the flute only.

5 play the piano only.
10 play both instruments.
A student is chosen at random.
What is the probability the student plays neither instrument?

Answer 1

5/27

Explanation:

I wrote it as a fraction, but the explanation is, if you're finding out how many who don't play instruments, you first need to find out who many do play instruments, so you add the numbers together.

10+5+7 = 22

So the probability that you'll pick one who does play an instrument would be 22/27 (because 22 out of the 27 pupils play an instrument.) But remember that's not what it's asking us for.

You have to subtract 27 - 22 to get the pupils who don't play instruments, you get 5, so the probability is 5/27 (5 pupils out of 27 don't play instruments.)

To put this in a percent, just divide the top number by the bottom number and move the decimal 2 places over, you get 18.5% or 19% both answers are correct depending on rounding.