During a single day at radio station WMZH, the probability that a particular song is played is 0.25 . What is the probability that this song will be played on exactly 6 days out of 6 days? Round your answer to the nearest thousandth. Answer:

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Identify Given Probability: Identify the given probability and the event. The probability that the song is played on any given day is 0.25. We want to find the probability that the song is played on exactly 6 out of 6 days.Recognize Distribution Type: Recognize the type of probability distribution. Since we are dealing with the probability of a song being played a certain number of times out of a fixed number of trials, this is a binomial probability distribution.Use Binomial Formula: Use the binomial probability formula. The binomial probability formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where: - P(X = k) is the probability of k successes in n trials, - (n choose k) is the binomial coefficient, - p is the probability of success on a single trial, - (1-p) is the probability of failure on a single trial.Calculate Probability: Calculate the probability using the binomial formula. For our problem, n = 6 (days), k = 6 (the song is played on exactly 6 days), and p = 0.25 (probability of the song being played on any given day). P(X = 6) = (6 choose 6) * 0.25^6 * (1-0.25)^(6-6)Evaluate Binomial Coefficient: Evaluate the binomial coefficient and simplify the expression. (6 choose 6) is 1 because there is only one way to choose 6 days out of 6. (1-0.25)^(6-6) is 1 because any number to the power of 0 is 1. So, P(X = 6) = 1 * 0.25^6 * 1Calculate Probability: Calculate the probability. P(X = 6) = 0.25^6 P(X = 6) = 0.25 * 0.25 * 0.25 * 0.25 * 0.25 * 0.25 P(X = 6) = 0.000244140625Round Answer: Round the answer to the nearest thousandth. P(X = 6) ≈ 0.000

During a single day at radio station WMZH, the probability that a particular song is played is $0$ . $25$ . What is the probability that this song will be played on exactly $6$ days out of $6$ days? Round your answer to the nearest thousandth. $\newline$ Answer:

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During a single day at radio station WMZH, the probability that a particular song is played is 000.252525 . What is the probability that this song will be played on exactly 666 days out of 666 days? Round your answer to the nearest thousandth.\newlineAnswer:

During a single day at radio station WMZH, the probability that a particular song is played is $0$ . $25$ . What is the probability that this song will be played on exactly $6$ days out of $6$ days? Round your answer to the nearest thousandth. $\newline$ Answer: