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 925 9 over 25 625 6 over 25 25 2 fifths 35
To calculate the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, you would use the formula:
P(Acoustic | Leather) = P(Acoustic and Leather) / P(Leather)
From the given table, we can see that 6 contestants played an acoustic guitar and wore leather pants.
P(Acoustic and Leather) = 6
From the table, we can see that there were a total of 6 contestants who wore leather pants.
P(Leather) = 6
Therefore, the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, is:
P(Acoustic | Leather) = 6 / 6 = 1
The conditional probability is 1, or 100%, that a randomly selected contestant played an acoustic guitar if they wore leather pants.