Five cards are drawn successively with replac | vedclass

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

Question

(A) Let $X$ represent the number of spade cards among the five cards drawn. Since the drawing of cards is with replacement,the trials are Bernoulli tr

Vedclass · Accepted Answer

$\frac{243}{1024}$

Vedclass · Answer

(A) Let $X$ represent the number of spade cards among the five cards drawn. Since the drawing of cards is with replacement,the trials are Bernoulli trials.In a well-shuffled deck of $52$ cards,there are $13$ spade cards.Probability of drawing a spade,$p = \frac{13}{52} = \frac{1}{4}$.Probability of not drawing a spade,$q = 1 - p = 1 - \frac{1}{4} = \frac{3}{4}$.$X$ follows a binomial distribution with $n = 5$ and $p = \frac{1}{4}$.The probability mass function is given by $P(X = x) = ^{n}C_{x} q^{n-x} p^{x}$,where $x = 0, 1, 2, 3, 4, 5$.We want to find the probability that none is a spade,which is $P(X = 0)$.$P(X = 0) = ^{5}C_{0} \cdot (\frac{3}{4})^{5-0} \cdot (\frac{1}{4})^{0}$.$P(X = 0) = 1 \cdot (\frac{3}{4})^{5} \cdot 1 = \frac{243}{1024}$.Thus,the probability that none of the cards is a spade is $\frac{243}{1024}$.

Five cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. What is the probability that none is a spade?

Similar Questions

Suppose $X$ follows a binomial distribution with parameters $n$ and $p$,where $0 < p < 1$. If $\frac{P(X=r)}{P(X=n-r)}$ is independent of $n$ for every $r$,then $p$ is equal to

Out of $100$ people selected at random,$10$ have a common cold. If five persons are selected at random from the group,then the probability that at most one person will have a common cold is

At least how many times must a fair coin be tossed so that the probability of getting at least one head is at least $0.8$?

If a dice is thrown twice,the probability of occurrence of $4$ at least once is

$A$ coin is tossed $7$ times. What is the probability that a person who calls 'heads' every time wins more often?

Vedclass Test Series

Exam Paper Generator

Online Exam Module