Question

a radio station will randomly select 1 of 5 playlists, each containing 8 songs, to play over the next hour. the station will then play the songs on the selected list in a random order. joshs favorite song is on 3 of those playlists. what is the probability that the first song in the next hour is joshs favorite song?
a 0.025
b 0.075
c 0.375
d 0.475

(then there are some radio buttons for selecting a, b, c, d, with a previous selection on as radio button)

Explanation:

Step1: Probability of selecting a playlist with the song

Probability = $\frac{\text{Number of playlists with the song}}{\text{Total playlists}} = \frac{3}{5}$

Step2: Probability the song is first in the playlist

Probability = $\frac{1}{\text{Songs per playlist}} = \frac{1}{8}$

Step3: Multiply the two probabilities

Total probability = $\frac{3}{5} \times \frac{1}{8} = \frac{3}{40} = 0.075$

Answer:

B. 0.075