Question

In a class of 27 students, 15 play an instrument and 13 play a sport. There are 5 students who play both an instrument and a sport. What is the probability that a student plays both an instrument and a sport?

Answer 1

To find the probability that a student plays both an instrument and a sport, we use the formula P(A and B) = P(A) * P(B|A). Substituting the given values, we get a probability of 5/27.

Step-by-step explanation:

To find the probability that a student plays both an instrument and a sport, we can use the formula:

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

Where:

• P(A) is the probability that a student plays an instrument (15/27)
• P(B) is the probability that a student plays a sport (13/27)
• P(B|A) is the probability that a student plays a sport given that they play an instrument (5/15)

Substituting the given values into the formula, we get:

P(A and B) = (15/27) * (5/15) = 5/27

Therefore, the probability that a student plays both an instrument and a sport is 5/27.