India and Pakistan play a 5-test hockey serie | vedclass

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(A) Let $n = 5$ be the number of games and $p = 1/2$ be the probability of winning a single game.India wins at least three games if they win $3, 4,$ o

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(A) Let $n = 5$ be the number of games and $p = 1/2$ be the probability of winning a single game.India wins at least three games if they win $3, 4,$ or $5$ games.Using the binomial probability formula $P(X = k) = {^nC_k} p^k q^{n-k}$,where $q = 1-p = 1/2$:$P(X \ge 3) = P(X=3) + P(X=4) + P(X=5)$$P(X \ge 3) = {^5C_3} (1/2)^5 + {^5C_4} (1/2)^5 + {^5C_5} (1/2)^5$$P(X \ge 3) = (10 + 5 + 1) 	imes (1/2)^5$$P(X \ge 3) = 16 	imes (1/32) = 1/2$.

India and Pakistan play a $5$-test hockey series. What is the probability that India wins at least three games?

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