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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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?

Similar Questions

In a box containing $100$ bulbs,$10$ are defective. The probability that out of a sample of $5$ bulbs,none is defective is

The probability of getting $4$ heads in $8$ throws of a coin is:

$A$ and $B$ are playing a chess game with each other. The probability that $A$ wins the game is $0.6$,the probability that he loses is $0.3$,and the probability that it is a draw is $0.1$. If they play three games,what is the probability that $A$ wins at least two games?

In a Binomial distribution $B(n, p)$,the sum and product of the mean and the variance are $5$ and $6$ respectively,then $6(n+p-q)=$

If the probability that a student is not a swimmer is $\frac{1}{5}$,then the probability that out of $5$ students one is a swimmer is

Vedclass Test Series

Exam Paper Generator

Online Exam Module