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Use binomial expansion to find the probability of getting 3 tails when flipping a coin 9
times.

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Final answer:

To find the probability of getting 3 tails when flipping a coin 9 times, we can use the binomial expansion formula. The probability is approximately 0.1641.

Step-by-step explanation:

To find the probability of getting 3 tails when flipping a coin 9 times, we can use the binomial expansion formula. The formula for the probability of getting exactly k successes in n independent trials is P(X=k) = nCk * p^k * (1-p)^(n-k), where nCk represents the binomial coefficient, p is the probability of success (getting a tail in this case), and (1-p) is the probability of failure (getting a head).

In this case, n = 9 and k = 3. The probability of getting a tail in a single coin flip is 0.5, so p = 0.5 and (1-p) = 0.5. Using the formula, we can calculate:

P(X=3) = 9C3 * 0.5^3 * 0.5^6 = 84 * 0.125 * 0.015625 ≈ 0.1641

Therefore, the probability of getting 3 tails when flipping a coin 9 times is approximately 0.1641.

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