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 the event that the contestant played an acoustic guitar, and B is the event that the contestant wore leather pants.
From the table given,
P(A and B) = 6 (number of contestants who played an acoustic guitar and wore leather pants)
P(B) = 6 + 9 = 15 (total number of contestants who wore leather pants)
Therefore, the conditional probability is:
P(A|B) = 6 / 15 = 2 / 5 = 2 fifths
So the correct response is 2 fifths.
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?
Responses
925
9
25
9 over 25 - no response given
35
3
5
3 fifths - no response given
625
6
25
6 over 25 - no response given
25
1 answer