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?

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:

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

where:
- P(A|B) is the conditional probability of A given B
- P(A and B) is the probability of both A and B happening
- P(B) is the probability of B happening

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

From the given data:
- Number of contestants wearing leather pants = 6 (leather pants)
- Number of contestants playing acoustic guitar and wearing leather pants = 6 (leather pants and acoustic guitar)

Now, we can substitute these values into the formula:

P(A|B) = (Number of contestants playing acoustic guitar and wearing leather pants) / (Number of contestants wearing leather pants)
P(A|B) = 6 / 6
P(A|B) = 1

So, the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, is 1 or 100%. This means that if a contestant is wearing leather pants, they definitely played an acoustic guitar.