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

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

Question

(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?

Similar Questions

From a lot of $30$ bulbs which include $6$ defectives,a sample of $4$ bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

The probability of a man hitting a target is $\frac{2}{3}$. What is the minimum number of times he must fire so that the probability of hitting the target at least once is more than $90 \%$?

$A$ random variable $X$ follows the binomial distribution and $X \sim B(n, 0.3)$. If the mean of $X$ is three times as large as the standard deviation of $X$,then $n=$

The mean and variance of a binomial distribution are $4$ and $3$ respectively. Then,the probability of getting exactly six successes in this distribution is:

If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$,then $P(|X-3| < 2)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module