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 that they play an instrument

Answer 1

The probability that a student does not play a sport given that they play an instrument after calculation is 1.29.

Step-by-step explanation:

To find the probability that a student does not play a sport given that they play an instrument, we can use conditional probability. The conditional probability of event A given event B can be calculated using the formula: P(A|B) = P(A and B) / P(B).

In this case, event A represents a student who does not play a sport, and event B represents a student who plays an instrument. We are given that 7 students play an instrument, 9 who play a sport, and 9 who do not play either.

Using these numbers, we can calculate the probability as follows:

P(Not playing a sport | Playing an instrument) = P(Not playing a sport and Playing an instrument) / P(Playing an instrument)

P(Not playing a sport and Playing an instrument) = 9 (given)

P(Playing an instrument) = 7 (given)

Therefore, P(Not playing a sport | Playing an instrument) = 9/7 = 1.29