If a fair coin is tossed five times,then the | vedclass

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(B) For a fair coin,the probability of getting a head in a single toss is $p = \frac{1}{2}$ and the probability of getting a tail is $q = 1 - p = \fra

Vedclass · Accepted Answer

$\frac{5}{16}$

Vedclass · Answer

(B) For a fair coin,the probability of getting a head in a single toss is $p = \frac{1}{2}$ and the probability of getting a tail is $q = 1 - p = \frac{1}{2}$.Since the coin is tossed $n = 5$ times,we use the binomial distribution formula: $P(X = k) = \binom{n}{k} p^k q^{n-k}$.We want the probability of getting exactly $k = 3$ heads.Substituting the values: $P(X = 3) = \binom{5}{3} (\frac{1}{2})^3 (\frac{1}{2})^{5-3}$.Calculating the binomial coefficient: $\binom{5}{3} = \frac{5 	imes 4}{2 	imes 1} = 10$.Thus,$P(X = 3) = 10 	imes (\frac{1}{2})^3 	imes (\frac{1}{2})^2 = 10 	imes (\frac{1}{2})^5$.$P(X = 3) = 10 	imes \frac{1}{32} = \frac{10}{32} = \frac{5}{16}$.Therefore,the correct option is $B$.

If a fair coin is tossed five times,then the probability of getting exactly three heads is . . . . . . .

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