Question

In a class of 20 students, 7 play an instrument and 9 play a sport. There are 9 students who do not play an instrument or a sport. What is the probability that a student does not play a sport given they play an instrument?

Answer 1

Let's denote:
- A = event that a student plays an instrument
- B = event that a student plays a sport

We know that there are 20 students in total, 7 play an instrument, 9 play a sport, and 9 do not play an instrument or a sport.

P(A) = 7/20
P(B) = 9/20
P(A ∩ B) = 20 - 9 = 11/20 (since 9 students do not play an instrument or a sport)

The probability that a student does not play a sport given they play an instrument is calculated by the conditional probability formula:

P(B' | A) = P(A ∩ B') / P(A)

P(B' | A) = [P(A) - P(A ∩ B)] / P(A)

P(B' | A) = (7/20 - 11/20) / 7/20
P(B' | A) = -4/20 / 7/20
P(B' | A) = -4/7

The probability that a student does not play a sport given they play an instrument is -4/7.