Question

During a single day at radio station WMZH, the probability that a particular song is played is 42%. What is the probability that this song will be played on at least 3 days out of 6 days? Round your answer to the nearest thousandth.

Answer 1

0.543 or 54.3%

Explanation:

This is an example of a binomial distribution, where the probability of success (playing the particular song) is 0.42, and the number of trials is 6.

To find the probability that the song will be played on at least 3 days out of 6, we need to calculate the probability of the song being played on 3, 4, 5, or 6 days.

Using a binomial probability calculator or formula, we can calculate these individual probabilities:

Probability of the song being played on 3 days out of 6: 0.308

Probability of the song being played on 4 days out of 6: 0.177

Probability of the song being played on 5 days out of 6: 0.052

Probability of the song being played on all 6 days: 0.006

To get the probability of the song being played on at least 3 days out of 6, we add these individual probabilities together:

0.308 + 0.177 + 0.052 + 0.006 = 0.543

Therefore, the probability that the song will be played on at least 3 days out of 6 is 0.543 or 54.3% (rounded to the nearest thousandth).