Question

Suppose that a high school marching band has 125 members. Of these 125 band members, 41 are seniors, 24 play the trumpet, and 10 are seniors who play the trumpet. What is the probability that a randomly selected band member is a senior given that he or she plays the trumpet

Answer 1

The probability that a senior is going to college and plays sports is 5/14.

Step-by-step explanation:

To calculate the probability that a senior is going to college and playing sports, we need to use the formula for conditional probability. The formula is:

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

In this case, we want to find the probability that a senior is going to college and plays sports, which is equivalent to finding the probability of being a senior who plays sports given that they are going to college.

We are given that 140 seniors are going to college and 50 of them are on the school's sports teams. So, the probability of being a senior who is going to college and plays sports is:

P(Senior goes to college and plays sports) = 50 / 140 = 5/14