If a fair coin is tossed 8 times, then the pr | vedclass

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(B) For a fair coin, the probability of getting a head is $p = 1/2$ and the probability of getting a tail is $q = 1/2$. The number of trials is $n = 8

Vedclass · Accepted Answer

$37/256$

Vedclass · Answer

(B) For a fair coin, the probability of getting a head is $p = 1/2$ and the probability of getting a tail is $q = 1/2$. The number of trials is $n = 8$.Using the binomial distribution formula $P(X = k) = \binom{n}{k} p^k q^{n-k}$, we need to find $P(X \le 2) = P(X=0) + P(X=1) + P(X=2)$.$P(X=0) = \binom{8}{0} (1/2)^8 = 1 	imes (1/256) = 1/256$.$P(X=1) = \binom{8}{1} (1/2)^8 = 8 	imes (1/256) = 8/256$.$P(X=2) = \binom{8}{2} (1/2)^8 = 28 	imes (1/256) = 28/256$.Summing these probabilities: $P(X \le 2) = (1 + 8 + 28) / 256 = 37/256$.

If a fair coin is tossed $8$ times, then the probability of getting at most $2$ heads is...

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