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
6
3
Electric guitar
9
7
What is the conditional probability that a randomly selected contestant played an acoustic guitar,
given they wore leather pants?
The answers are:
3/5
2/5
6/25
9/25
To find the conditional probability that a randomly selected contestant played an acoustic guitar given they wore leather pants, we need to find the number of contestants who wore leather pants and played an acoustic guitar, and then divide that by the total number of contestants who wore leather pants.
From the information given:
- 6 contestants played the acoustic guitar
- 9 contestants played the electric guitar
- 3 contestants wore leather pants
Of the 3 contestants who wore leather pants, 6 of them played the acoustic guitar
So the conditional probability is:
Number of contestants who played an acoustic guitar and wore leather pants / Number of contestants who wore leather pants
= 6 / 3
= 2/5
Therefore, the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, is 2/5.