Question

a class of 22 students, 13 play an instrument and 7 play a sport. There are 5 students who play an instrument and also play a sport. What is the probability that a student does not play a sport given that they play an instrument? Write your answer as a simplified fraction or as a decimal rounded to 3 decimal places ( 1 point) The probability that a student does not play a sport given that they play an instrument is

Answer 1

0.385

To find the probability that a student does not play a sport given that they play an instrument, we use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

In this case, A represents not playing a sport and B represents playing an instrument.

We know that there are 5 students who play both an instrument and a sport, so P(A and B) = 5/22.
There are 13 students who play an instrument, so P(B) = 13/22.

Therefore, the probability that a student does not play a sport given that they play an instrument is:

P(A|B) = (5/22) / (13/22) = 5/13 ≈ 0.385