A coin is tossed 3 times by 2 persons. What i | vedclass

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(C) Let $A$ and $B$ be the two persons. Each tosses a coin $3$ times.The probability of getting $r$ heads in $3$ tosses follows a binomial distributio

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$\frac{5}{16}$

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(C) Let $A$ and $B$ be the two persons. Each tosses a coin $3$ times.The probability of getting $r$ heads in $3$ tosses follows a binomial distribution $P(X=r) = \binom{3}{r} (\frac{1}{2})^3$.For $r = 0, 1, 2, 3$,the probabilities are:$P(0) = \binom{3}{0} (\frac{1}{8}) = \frac{1}{8}$$P(1) = \binom{3}{1} (\frac{1}{8}) = \frac{3}{8}$$P(2) = \binom{3}{2} (\frac{1}{8}) = \frac{3}{8}$$P(3) = \binom{3}{3} (\frac{1}{8}) = \frac{1}{8}$Since the events are independent,the probability that both get an equal number of heads is the sum of the probabilities of both getting $0, 1, 2,$ or $3$ heads:$P = P(0)P(0) + P(1)P(1) + P(2)P(2) + P(3)P(3)$$P = (\frac{1}{8} 	imes \frac{1}{8}) + (\frac{3}{8} 	imes \frac{3}{8}) + (\frac{3}{8} 	imes \frac{3}{8}) + (\frac{1}{8} 	imes \frac{1}{8})$$P = \frac{1}{64} + \frac{9}{64} + \frac{9}{64} + \frac{1}{64} = \frac{20}{64} = \frac{5}{16}$.

$A$ coin is tossed $3$ times by $2$ persons. What is the probability that both get an equal number of heads?

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