Question

In a group of 24 pupils, 13 play the flute only. 2 play the piano only. 1 plays both instruments. A student is chosen at random. What is the probability the student plays neither instrument?

Answer 1

The probability the student plays neither instrument is 33.3%

Explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases.

`P(A)=(number of favorable cases)/(number of possible cases)`

The total number of pupils who play at least one instrument is:

13 + 2 + 1 = 16

The means there are 24 - 16 = 8 pupils who play neither of the instruments.

So you know:

• number of favorable cases: 8
• number of possible cases: 24

Replacing in the definition:

`P(A)=(8)/(24)`

`P(A)=(1)/(3)`

P(A)= 0.333= 33.3%

The probability the student plays neither instrument is 33.3%