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(C) When $8$ coins are tossed simultaneously,the total number of possible outcomes is $2^8 = 256$. Let $X$ be the number of heads obtained. $X$ follow

Vedclass · Accepted Answer

$\frac{37}{256}$

Vedclass · Answer

(C) When $8$ coins are tossed simultaneously,the total number of possible outcomes is $2^8 = 256$. Let $X$ be the number of heads obtained. $X$ follows a binomial distribution with $n = 8$ and $p = 0.5$. The probability of getting at least $6$ heads is $P(X \ge 6) = P(X = 6) + P(X = 7) + P(X = 8)$. Using the formula $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$,we have: $P(X = 6) = \binom{8}{6} (0.5)^8 = 28 	imes \frac{1}{256} = \frac{28}{256}$. $P(X = 7) = \binom{8}{7} (0.5)^8 = 8 	imes \frac{1}{256} = \frac{8}{256}$. $P(X = 8) = \binom{8}{8} (0.5)^8 = 1 	imes \frac{1}{256} = \frac{1}{256}$. Summing these probabilities: $P(X \ge 6) = \frac{28 + 8 + 1}{256} = \frac{37}{256}$.

If $8$ coins are tossed simultaneously,then the probability of getting at least $6$ heads is

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