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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
25
9 over 25
35
3
5
3 fifths
625
6
25
6 over 25
25
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)
First, we need to find P(A and B), the probability of a contestant playing an acoustic guitar and wearing leather pants. From the table, we see that there were 6 contestants who played an acoustic guitar and wore leather pants.
P(A and B) = 6
Next, we need to find P(B), the probability of a contestant wearing leather pants. From the table, we see that there were a total of 6 + 9 = 15 contestants who wore leather pants.
P(B) = 6 + 9 = 15
Now we can calculate the conditional probability:
P(A|B) = P(A and B) / P(B) = 6 / 15 = 2 / 5 = 2 over 5
Therefore, the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, is 2 over 5.