Question

During a single day at radio station WMZH, the probability that a particular song is played is 4/5. What is the probability that this song will be played on exactly 2 days out of 3 days? Round your answer to the nearest thousandth.

Answer 1

The probability that the song will be played on exactly 2 days out of 3 days is approximately 0.384.

Step-by-step explanation:

To find the probability that the song will be played on exactly 2 days out of 3, we can use the binomial probability formula. The formula is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where P(X=k) is the probability of getting exactly k successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient. In this case, n = 3 (3 days), k = 2 (2 days), and p = 4/5. Plugging these values into the formula, we get:

P(X=2) = (3 choose 2) * (4/5)^2 * (1-4/5)^(3-2)

P(X=2) = 3 * (4/5)^2 * (1/5)

P(X=2) = 3 * (16/25) * (1/5)

P(X=2) = 48/125

Therefore, the probability that the song will be played on exactly 2 days out of 3 days is approximately 0.384 (rounded to the nearest thousandth).