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 $\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$.

$X = x$	$1$	$2$	$3$	$\dots$	$n$
$P(X = x)$	$\frac{1}{n}$	$\frac{1}{n}$	$\frac{1}{n}$	$\dots$	$\frac{1}{n}$

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

It is known that a box of $8$ batteries contains $3$ defective pieces and a person randomly selects two batteries from the box. If $X$ is the number of defective batteries selected,then $P(X \leq 1) = $

In a city,$10$ accidents take place in a span of $50$ days. Assuming that the number of accidents follows the Poisson distribution,the probability that three or more accidents occur in a day is:

In a game,$3$ coins are tossed. $A$ person is paid $₹150$ if he gets all heads or all tails,and he is supposed to pay $₹50$ if he gets one head or two heads. The amount he can expect to win or lose on an average per game in $₹$ is:

Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable $X$ to be the number of rotten apples in a draw of two apples,the variance of $X$ is

The probability distribution of a random variable $X$ is given by the following table:
$X = x$ $1$ $2$ $3$ $\dots$ $n$
$P(X = x)$ $\frac{1}{n}$ $\frac{1}{n}$ $\frac{1}{n}$ $\dots$ $\frac{1}{n}$

Then $\operatorname{Var}(X) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module