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 person tosses a coin $3$ times. The number of heads obtained by each person follows a binomial distributi

Vedclass · Accepted Answer

$\frac{5}{16}$

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(C) Let $A$ and $B$ be the two persons. Each person tosses a coin $3$ times. The number of heads obtained by each person follows a binomial distribution $B(n=3, p=1/2)$.The probability of getting $k$ heads is given by $P(X=k) = \binom{3}{k} (1/2)^3$.$P(X=0) = \binom{3}{0} \frac{1}{8} = \frac{1}{8}$$P(X=1) = \binom{3}{1} \frac{1}{8} = \frac{3}{8}$$P(X=2) = \binom{3}{2} \frac{1}{8} = \frac{3}{8}$$P(X=3) = \binom{3}{3} \frac{1}{8} = \frac{1}{8}$The condition is satisfied if both get $0, 1, 2,$ or $3$ heads.Required probability $= P(A=0)P(B=0) + P(A=1)P(B=1) + P(A=2)P(B=2) + P(A=3)P(B=3)$$= \left( \frac{1}{8} 	imes \frac{1}{8} ight) + \left( \frac{3}{8} 	imes \frac{3}{8} ight) + \left( \frac{3}{8} 	imes \frac{3}{8} ight) + \left( \frac{1}{8} 	imes \frac{1}{8} ight)$$= \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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