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

$A$ box contains $25$ tickets numbered $1, 2, \dots, 25$. If two tickets are drawn at random,then the probability that the product of their numbers is even is:

Three numbers are chosen at random without replacement from the set $A = \{x \in \mathbb{Z} \mid 2 \leq x \leq 11\}$. The probability that the minimum of the chosen numbers is $3$ and the maximum is $7$ is

If a committee of $3$ is to be chosen from a group of $38$ people of which you are a member,what is the probability that you will be on the committee?

$A$ box contains $8$ red and $x$ number of green balls. $3$ balls are drawn at random. If the probability that all $3$ balls are red is $\frac{7}{15}$,then the number of green balls $x$ is:

$3$ bulbs are drawn at random from a lot of $50$ bulbs,$5$ of which are defective. Find the probability of the event that all $3$ bulbs are non-defective (drawn without replacement).

Vedclass Test Series

Exam Paper Generator

Online Exam Module