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?
(1 point)
Leather
Velvet
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 calculate the number of contestants who played an acoustic guitar and wore leather pants, and then divide it by the total number of contestants who wore leather pants.
From the information given:
- 6 contestants played an acoustic guitar
- 3 contestants played an acoustic guitar and wore leather pants
- 9 contestants played an electric guitar
- 7 contestants played an electric guitar and wore leather pants
So, the total number of contestants who wore leather pants is 3 (contesting playing acoustic guitar) + 7 (contestants playing electric guitar) = 10.
The number of contestants who played an acoustic guitar and wore leather pants is 3.
Therefore, the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants is 3/10 or 3/10 = 3/10.