Two cards are drawn successively with replace | vedclass

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

Question

(D) The probability of drawing a king card in a single draw is $p = \frac{4}{52} = \frac{1}{13}$.The probability of not drawing a king is $q = 1 - \fr

Vedclass · Accepted Answer

$\frac{25}{169}$

Vedclass · Answer

(D) The probability of drawing a king card in a single draw is $p = \frac{4}{52} = \frac{1}{13}$.The probability of not drawing a king is $q = 1 - \frac{1}{13} = \frac{12}{13}$.Since the cards are drawn with replacement,this follows a binomial distribution with $n = 2$ and $p = \frac{1}{13}$.$P(X=k) = \binom{n}{k} p^k q^{n-k}$.For $X=1$: $P(X=1) = \binom{2}{1} \left(\frac{1}{13}ight)^1 \left(\frac{12}{13}ight)^1 = 2 	imes \frac{12}{169} = \frac{24}{169}$.For $X=2$: $P(X=2) = \binom{2}{2} \left(\frac{1}{13}ight)^2 \left(\frac{12}{13}ight)^0 = 1 	imes \frac{1}{169} = \frac{1}{169}$.Therefore,$P(X=1) + P(X=2) = \frac{24}{169} + \frac{1}{169} = \frac{25}{169}$.

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. Let $X$ denote the random variable of the number of kings obtained in the two drawn cards. Then $P(X=1) + P(X=2)$ equals:

Similar Questions

If $7$ different balls are distributed among $4$ different boxes,then the probability that the first box contains $3$ balls is

The probability that a marksman will hit a target is given as $1/5$. Then his probability of at least one hit in $10$ shots is:

It is observed that $25\%$ of the cases related to child labour reported to the police station are solved. If $6$ new cases are reported,then the probability that at least $5$ of them will be solved is . . . . . .

Numbers are selected at random,one at a time from the two-digit numbers $00, 01, 02, \dots, 99$ with replacement. An event $E$ occurs only if the product of the two digits of a selected number is $24$. If four numbers are selected,then the probability that the event $E$ occurs at least $3$ times 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