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Question

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

925
9 over 25

625
6 over 25

25
2 fifths

35

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 is "played an acoustic guitar" and B is "wore leather pants."

From the table, we see that 6 contestants played an acoustic guitar and wore leather pants.

So P(A and B) = 6

We also see that there were a total of 6 + 9 = 15 contestants who wore leather pants.

So P(B) = 15

Therefore, the conditional probability is:

P(A | B) = 6 / 15 = 2/5 = 0.4

So the answer is 2/5 or 0.4.