what's the fraction 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 find the conditional probability that a randomly selected contestant played an acoustic guitar given they wore leather pants, we need to use the formula:
Conditional Probability (A|B) = P(A and B) / P(B)
In this case:
- P(A and B) is the number of contestants who played an acoustic guitar and wore leather pants, which is 6.
- P(B) is the total number of contestants who wore leather pants, which is 6 + 9 = 15.
So the conditional probability is:
6 / 15 = 2/5
Therefore, the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, is 2/5.