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

From a well-shuffled pack of $52$ cards,two cards are drawn at random. The probability that both cards are kings is:

$A$ seven-digit number is formed using the digits $3, 3, 4, 4, 4, 5, 5$. The probability that the number so formed is divisible by $2$ is ..... .

On her vacations,Veena visits four cities ($A, B, C$,and $D$) in a random order. What is the probability that she visits $A$ before $B$ and $B$ before $C$?

If all the letters of the word $MISSISSIPPI$ are rearranged,what is the probability that all $S$ come together?

Four boys and three girls stand in a queue for an interview. What is the probability that they will be in alternate positions?

Vedclass Test Series

Exam Paper Generator

Online Exam Module