A and B are two tennis players of equal skill | vedclass

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(C) Since $A$ and $B$ are equally skilled,the probability of $A$ winning a single game is $p = 1/2$.The probability of $A$ winning exactly $k = 3$ gam

Vedclass · Accepted Answer

$1/4$

Vedclass · Answer

(C) Since $A$ and $B$ are equally skilled,the probability of $A$ winning a single game is $p = 1/2$.The probability of $A$ winning exactly $k = 3$ games out of $n = 4$ games follows the binomial distribution formula:$P(X = k) = { }^n C_k p^k (1-p)^{n-k}$Substituting the values:$P(X = 3) = { }^4 C_3 \left(\frac{1}{2}ight)^3 \left(1-\frac{1}{2}ight)^{4-3}$$P(X = 3) = 4 	imes \left(\frac{1}{8}ight) 	imes \left(\frac{1}{2}ight)$$P(X = 3) = 4 	imes \frac{1}{16} = \frac{1}{4}$

$A$ and $B$ are two tennis players of equal skill. If they play $4$ games,what is the probability that $A$ wins exactly three games?

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