Suppose that a high school marching band has 86 members. Of these 86 band members, 26 are seniors, 17 play the trumpet, and 4 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? Give your answer as a percentage, rounded to one decimal place. What is the probability that a randomly selected band member plays the trumpet given that he or she is a senior?

a) 0.4117 = 41.2% to 1 d.p

b) 0.2693 = 26.9% to 1 d.p

Step-by-step explanation:

Total number of members of the marching band = n(U) = 86

Number of seniors in the marching band = n(S) = 26

Number of trumpet players in the marching band = n(T) = 17

Number of seniors who are trumpet players in the marching band = n(S n T) = 4

Probability that a randomly selected member of the marching band is a senior = P(S) = (26/86) = 0.3023

Probability that a randomly selected member of the marching band is a trumpet player = P(T) = (17/86) = 0.1977

Probability that a randomly selected member of the marching band is a senior and a trumpet player = P(S n T) = (7/86) = 0.0814

a) The probability that a randomly selected band member is a senior given that he or she plays the trumpet is the conditional probability, P(S|T)

Mathematically. It is given as

P(S|T) = P(S n T)/P(T)

P(S|T) = (0.0814/0.1977)

P(S|T) = 0.4117 = 41.2% to 1 d.p

b) The probability that a randomly selected band member plays the trumpet given that he or she is a senior = P(T|S)

P(T|S) = P(S n T)/P(S)

P(T|S) = (0.0814/0.3023)

P(T|S) = 0.2693 = 26.9%

Hope this Helps!!!