If a fair die is rolled 7 times, what is the probability, to the nearest thousandth, of getting exactly 1 two? Answer:

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Determine Probability of Two: Determine the probability of rolling a two on a single roll of a fair die. A fair die has six faces, so the probability of rolling any specific number, including a two, is 1 out of 6.Determine Probability of Not Two: Determine the probability of not rolling a two on a single roll of a fair die. Since there are five other outcomes that are not a two, the probability of not rolling a two is 5 out of 6.Calculate Probability of One Two in Seven Rolls: Calculate the probability of rolling exactly one two in seven rolls. This event can happen in several different ways: the two can appear on the first roll, the second roll, and so on, up to the seventh roll. For each case, the other six rolls must not be a two.Use Binomial Probability Formula: Use the binomial probability formula to calculate the probability of exactly one success (rolling a two) in seven trials (rolls). 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.Plug Values into Formula: Plug the values into the binomial probability formula. Here, n=7 (number of trials), k=1 (number of successes), p=1/6 (probability of rolling a two), and (1-p)=5/6 (probability of not rolling a two). P(X=1) = (7 choose 1) * (1/6)^1 * (5/6)^(7-1)Calculate Binomial Coefficient: Calculate the binomial coefficient (7 choose 1). (7 choose 1) is the number of ways to choose 1 success (rolling a two) out of 7 trials, which is simply 7.Perform Calculations: Perform the calculations. P(X=1) = 7 * (1/6)^1 * (5/6)^6 P(X=1) = 7 * (1/6) * (5/6)^6Calculate Exact Probability: Calculate the exact probability. P(X=1) = 7 * (1/6) * (15625/46656) (since (5/6)^6 = 15625/46656) P(X=1) = 7 * (1/6) * (15625/46656) P(X=1) = 7 * 15625 / (6 * 46656) P(X=1) = 109375 / 279936Simplify Fraction and Round: Simplify the fraction and round to the nearest thousandth. P(X=1) ≈ 0.391 (rounded to three decimal places)

If a fair die is rolled $7$ times, what is the probability, to the nearest thousandth, of getting exactly $1$ two? $\newline$ Answer:

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If a fair die is rolled $7$ times, what is the probability, to the nearest thousandth, of getting exactly $1$ two? $\newline$ Answer: