Probability that three cards drawn from a pack of 52 cards are all red is

English

Gujarati

Hindi

14.Probability

easy

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

A

$\frac{1}{{17}}$

B

$\frac{3}{{19}}$

C

$\frac{2}{{19}}$

D

$\frac{2}{{17}}$

Solution

(d) $3$ cards are drawn out of $26$ red cards (favourable)

$ = \frac{{{}^{26}{C_3}}}{{{}^{52}{C_3}}} = \frac{{26\,\,!}}{{3\,\,!\,\,23\,\,!}} \times \frac{{3\,\,!\,\,49\,\,!}}{{52\,\,!}} = \frac{2}{{17}}.$

Standard 11

Mathematics

Share

Similar Questions

$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and one spade?

medium

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained in the $(i-1)^{\text {th }}$ roll, $i=2,3$, is equal to :

medium

(JEE MAIN-2024)

A card is drawn from a pack of $52$ playing cards. The card is replaced and pack is shuffled. If this is done six times, then the probability that $2$ hearts, $2$ diamond and $2$ black cards are drawn is

normal

Find the probability that when a hand of $7$ cards is drawn from a well shuffled deck of $52$ cards, it contains $3$ Kings.

medium

Two integers are selected at random from the set $\{1, 2, …, 11\}.$ Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

hard

(JEE MAIN-2019)