Question

In a group of 28 pupils, 12 play the flute only.

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

Answer 1

Explanation:

we have 28 students in total.

9 do not play any instrument.

that means 19 students play at least one instrument.

12 play only the flute.

6 play only the piano.

that is 12+6 = 18 together.

but we have 19 players.

so, 1 student must play both, the flute and the piano.

remember, a probability is always

desired cases / possible cases

when we are looking for the students that play both instruments, we have only 1 out of the possible 28 cases.

and the probabilty to pick this student randomly is

1/28 = 0.035714286...