When a coin is tossed 6 times,the probability | vedclass

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(D) Total number of outcomes when a coin is tossed $6$ times is $2^6 = 64$. Let $X$ be the number of heads. We want the probability $P(X > 3)$,which m

Vedclass · Accepted Answer

$\frac{11}{32}$

Vedclass · Answer

(D) Total number of outcomes when a coin is tossed $6$ times is $2^6 = 64$. Let $X$ be the number of heads. We want the probability $P(X > 3)$,which means $X$ can be $4, 5,$ or $6$. The number of ways to get $r$ heads in $n$ tosses is given by $\binom{n}{r}$. Number of ways to get $4$ heads $= \binom{6}{4} = \frac{6!}{4!2!} = 15$. Number of ways to get $5$ heads $= \binom{6}{5} = \frac{6!}{5!1!} = 6$. Number of ways to get $6$ heads $= \binom{6}{6} = \frac{6!}{6!0!} = 1$. Total favorable outcomes $= 15 + 6 + 1 = 22$. Required Probability $= \frac{22}{64} = \frac{11}{32}$. Hence,option $D$ is correct.

When a coin is tossed $6$ times,the probability of getting more heads than tails is

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