During a single day at radio station WMZH, the probability that a particular song is played is 0.15. What is the probability that this song will be played on exactly 5 days out of 7 days? Round your answer to the nearest thousandth.

0.001

Step-by-step explanation:

This is a combination problem, so we need to calculate the combination of 7 choose 5, and then multiply by the probability of each event:

Combination of 7 choose 5:

C(7,5) = 7! / (5! * 2!) = 7*6/2 = 21

This value means that we have 21 different possibilities of the 5 days we want being allocated in the 7 days

Now, the probability of each event is:

5 days playing the song: (0.15)^5

2 days not playing the song: (0.85)^2

So, the final probability is

P = C(7,5) * (0.15)^5 * (0.85)^2 = 0.001