If P and Q each toss three coins,the probabil | vedclass

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(D) Let $X$ be the number of heads obtained by $P$ and $Y$ be the number of heads obtained by $Q$. Both $X$ and $Y$ follow a binomial distribution $B(

Vedclass · Accepted Answer

$\frac{5}{16}$

Vedclass · Answer

(D) Let $X$ be the number of heads obtained by $P$ and $Y$ be the number of heads obtained by $Q$. Both $X$ and $Y$ follow a binomial distribution $B(n=3, p=0.5)$.The probability of getting $r$ heads in $3$ tosses is given by $P(X=r) = ^{3}C_{r} (0.5)^3$.We want to find $P(X=Y) = \sum_{r=0}^{3} P(X=r) 	imes P(Y=r)$.Since $P(X=r) = P(Y=r)$,this becomes $\sum_{r=0}^{3} [P(X=r)]^2$.$P(X=0) = ^{3}C_{0} (0.5)^3 = \frac{1}{8}$,$P(X=1) = ^{3}C_{1} (0.5)^3 = \frac{3}{8}$,$P(X=2) = ^{3}C_{2} (0.5)^3 = \frac{3}{8}$,$P(X=3) = ^{3}C_{3} (0.5)^3 = \frac{1}{8}$.$P(X=Y) = (\frac{1}{8})^2 + (\frac{3}{8})^2 + (\frac{3}{8})^2 + (\frac{1}{8})^2 = \frac{1+9+9+1}{64} = \frac{20}{64} = \frac{5}{16}$.Thus,option $D$ is correct.

If $P$ and $Q$ each toss three coins,the probability that both get the same number of heads is

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