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what is the probability of getting exactly 4 heads when flipping a coin 6 times

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What is the probability of getting exactly 4 heads when flipping a coin 6 times?

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Answer to a math question What is the probability of getting exactly 4 heads when flipping a coin 6 times?

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P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

n = 6

k = 4

p = 0.5

\binom{6}{4} = 15

P(X = 4) = 15 \cdot (0.5)^4 \cdot (0.5)^2

P(X = 4) = 15 \cdot (0.5)^6

P(X = 4) = 15 \cdot \frac{1}{64}

P(X = 4) = \frac{15}{64}

P(X = 4) \approx 0.2344

P(X = 4) = \frac{15}{64}

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