During a single day at radio station WMZH, the probability that a particular song is played is 1//6. What is the probability that this song will be played on exactly 3 days out of 4 days? Round your answer to the nearest thousandth. Answer:

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During a single day at radio station WMZH, the probability that a particular song is played is  1//6. What is the probability that this song will be played on exactly 3 days out of 4 days? Round your answer to the nearest thousandth. Answer:

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Understand and Determine Probability: Understand the problem and determine the probability of the song being played on any given day. The probability of the song being played on a single day is given as 1/6. We need to find the probability of this event happening exactly 3 times in a sequence of 4 days.Use Binomial Probability Formula: Use the binomial probability formula to calculate the probability of the song being played exactly 3 times in 4 days. 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, and - (1-p) is the probability of failure on a single trial. In this case, n=4, k=3, and p=1/6.Calculate Binomial Coefficient: Calculate the binomial coefficient (4 choose 3). (4 choose 3) = 4! / (3! * (4-3)!) = 4 / 1 = 4.Calculate Probability of 3 Times: Calculate the probability of the song being played exactly 3 times. Using the binomial probability formula: P(X=3) = (4 choose 3) * (1/6)^3 * (5/6)^(4-3) P(X=3) = 4 * (1/6)^3 * (5/6)^1Perform Calculations: Perform the calculations. P(X=3) = 4 * (1/216) * (5/6) P(X=3) = 4 * 1/216 * 5/6 P(X=3) = 20/1296Simplify Fraction and Round: Simplify the fraction and round to the nearest thousandth. 20/1296 can be simplified to 5/324. To round to the nearest thousandth, we convert 5/324 to a decimal. 5/324 ≈ 0.015432098765432098... Rounded to the nearest thousandth, this is approximately 0.015.

During a single day at radio station WMZH, the probability that a particular song is played is $1 / 6$ . What is the probability that this song will be played on exactly $3$ days out of $4$ 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 $1 / 6$ . What is the probability that this song will be played on exactly $3$ days out of $4$ days? Round your answer to the nearest thousandth. $\newline$ Answer: