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If a fair coin is tossed 5 times, what is the probability, to the nearest thousandth, of getting exactly 3 tails?

Answer

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Answer

Calculate probability: \( P(X=3) = 10 \times 0.125 \times 0.25 = 0.3125 \)

Steps

Step 1 ：Use the binomial probability formula: \( P(X=k) = \binom{n}{k} p^{k}(1-p)^{n-k} \)

Step 2 ：Substitute values: \( P(X=3) = \binom{5}{3} 0.5^{3}(1-0.5)^{5-3} \)

Step 3 ：Calculate probability: \( P(X=3) = 10 \times 0.125 \times 0.25 = 0.3125 \)