The probability that three cards drawn from a | vedclass

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

Question

(D) The total number of ways to draw $3$ cards from a pack of $52$ cards is given by ${}^{52}C_3$. There are $26$ red cards in a pack of $52$. The num

Vedclass · Accepted Answer

$\frac{2}{17}$

Vedclass · Answer

(D) The total number of ways to draw $3$ cards from a pack of $52$ cards is given by ${}^{52}C_3$. There are $26$ red cards in a pack of $52$. The number of ways to draw $3$ red cards is ${}^{26}C_3$. $	ext{Required probability} = \frac{{}^{26}C_3}{{}^{52}C_3} = \frac{\frac{26 	imes 25 	imes 24}{3 	imes 2 	imes 1}}{\frac{52 	imes 51 	imes 50}{3 	imes 2 	imes 1}} = \frac{26 	imes 25 	imes 24}{52 	imes 51 	imes 50}$. Simplifying the expression: $\frac{26}{52} 	imes \frac{25}{50} 	imes \frac{24}{51} = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{8}{17} = \frac{8}{68} = \frac{2}{17}$.

The probability that three cards drawn from a pack of $52$ cards are all red is

Similar Questions

If $m$ rupee coins and $n$ ten paise coins are placed in a line,then the probability that the extreme coins are ten paise coins is

$A$ five-digit number is formed by the digits $1, 2, 3, 4, 5$ with no digit being repeated. The probability that the number is divisible by $4$ is

From a class of $12$ girls and $18$ boys,two students are chosen randomly. What is the probability that both of them are girls?

$4$ boys and $2$ girls occupy seats in a row at random. The probability that the two girls occupy seats side by side is:

If the letters of the word $ASSASSIN$ are arranged in a row at random,what is the probability that no two $S$s occur together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module