Be sure you are writing out your steps. You will have to submit your shown work for each problem at the end Riley was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Riley recorded which type of guitar each contestant played. He also counted the number of contestants wearing different kinds of pants, as there were some interesting stylistic choices. Acoustic guitar Electric guitar Leather 6 9 Velvet 3 7 What is the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants? (1 point) Responses 25 2 fifths 625 6 over 25 35 3 fifths 925

Answer 1

To find the conditional probability that a randomly selected contestant played an acoustic guitar given they wore leather pants, we use the formula for conditional probability:

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

In this case, A represents playing an acoustic guitar and B represents wearing leather pants.

First, we need to find the probabilities of A and B:

P(A and B) = Number of contestants who played an acoustic guitar and wore leather pants / Total number of contestants = 6 / (6 + 9) = 6 / 15 = 2/5

P(B) = Number of contestants who wore leather pants / Total number of contestants = 15 / (6 + 9 + 3 + 7) = 15 / 25 = 3/5

Now, plug these values into the formula for conditional probability:

P(A|B) = P(A and B) / P(B) = (2/5) / (3/5) = 2/5 * 5/3 = 2/3

Therefore, the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, is 2/3.