The probability of India winning a test match | vedclass

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

Question

(C) Let $p$ be the probability of winning a match,$p = \frac{1}{2}$.Let $q$ be the probability of losing a match,$q = 1 - p = \frac{1}{2}$.For India's

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(C) Let $p$ be the probability of winning a match,$p = \frac{1}{2}$.Let $q$ be the probability of losing a match,$q = 1 - p = \frac{1}{2}$.For India's second win to occur at the third test,India must win exactly one match in the first two tests and win the third test.The possible sequences for the first three matches are $(L, W, W)$ and $(W, L, W)$.The probability of the sequence $(L, W, W)$ is $q 	imes p 	imes p = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{8}$.The probability of the sequence $(W, L, W)$ is $p 	imes q 	imes p = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{8}$.The total probability is $\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$.

$X$	$1$	$2$	$3$	$4$	$5$	$6$
$F(X=x)$	$0.2$	$0.37$	$0.48$	$0.62$	$0.85$	$1$

The probability of India winning a test match against West Indies is $\frac{1}{2}$. Assuming independence from match to match,the probability that in a $5$ match series India's second win occurs at the third test,is

Similar Questions

If $X$ is a Poisson variate with $P(X=0)=0.8$, then the variance of $X$ is

If a random variable $X$ denotes the number that appears on the upper face of a die when it is rolled,then $\frac{\text{Variance of } X}{\text{Mean of } X}$ is equal to

The cumulative distribution function $F(X)$ of a discrete random variable $X$ is given by the following table:
$X$ $1$ $2$ $3$ $4$ $5$ $6$
$F(X=x)$ $0.2$ $0.37$ $0.48$ $0.62$ $0.85$ $1$

Then $P[X=4] + P[X=5] = $

Let a random variable $X$ take values $\{0, 1, 2, 3\}$ with $P(X=0) = P(X=1) = p$,$P(X=2) = P(X=3) = q$,and $E(X^2) = 2E(X)$. Then the value of $8p - 1$ is:

The variance of the following probability distribution is:
$x$ $0$ $1$ $2$
$P(X)$ $\frac{9}{16}$ $\frac{3}{8}$ $\frac{1}{16}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module