Question

In a class of 29 students, 24 play an instrument, and 13 play a sport. There are 3 students who do not play an instrument or a sport. What is the probability that a student who plays an instrument also plays a sport?

A) 0.45
B) 0.65
C) 0.75
D) 0.85

Answer 1

The probability that a student who plays an instrument also plays a sport is C)0.75.

Step-by-step explanation:

To find the probability that a student who plays an instrument also plays a sport, we need to use the concept of conditional probability. We know that there are 29 students in total, 24 of whom play an instrument, 13 play a sport, and 3 students do not play either. Let's represent the event of playing an instrument as A and the event of playing a sport as B.

The probability that a student plays an instrument given that they play a sport, denoted as P(A|B), can be found using the formula:

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

Given that 3 students do not play either, there are 29 - 3 = 26 students who play either an instrument or a sport. Therefore, P(B) = 26/29.

Since we are given that there are 24 students who play an instrument and 13 students who play a sport, but 3 students do not play either, we can calculate P(A and B) as:

P(A and B) = 24 - 3 = 21.

Now we can substitute the values into the formula to find P(A|B):

P(A|B) = 21 / (26/29) = 21 * (29/26) = 0.75.

Therefore, the probability that a student who plays an instrument also plays a sport is 0.75, which corresponds to option C.