Question

During a single day at radio station WMZH,the probability that a particular song is played is 0.6. what is the probability that this song will be played on at least 3 days out of 4 days?

Answer 1

The probability that the song will be played on at least 3 days out of 4 days is approximately 0.9744 or 97.44%.

Here's how to calculate the probability of the song being played on at least 3 days out of 4 days at radio station WMZH:

Complementary approach: Instead of calculating the probability directly, we can find the probability of the song NOT being played on at least 3 days and then subtract it from 1 (total probability).

Probability of the song NOT being played on a single day: This is given as 1 - 0.6 = 0.4.

Probability of the song NOT being played on all 4 days: This is (0.4)⁴ = 0.0256.

Probability of the song being played on at least 3 days: This is 1 - 0.0256 = 0.9744.

Therefore, the probability that the song will be played on at least 3 days out of 4 days is approximately 0.9744 or 97.44%.