Question

In a group of 47 pupils, 14 play the flute only.

8 play the piano only.
14 play neither instrument.
A student is selected at random.
What is the probability the student plays both instruments?

Answer 1

The total number of students who play at least one instrument is 10 + 12 + 6 = 28. The means there are 32 - 28 = 4 students who play neither of the instruments. Therefore, the probability that a student plays neither instrument is 4/32 = 1/8 = 0.125 = 12.5%.

Answer 2

11/47

Explanation:

Total number of pupils = 47

We are told that 14 play the flute only, 8 play the piano only and 14 play neither instrument.

So adding these together: 14 + 8 + 14 = 36

To find the number that played both instruments: 47 - 36 = 11

So 11 pupils play both instruments

The probability is the value divided by the total: 11/47