If 2 cards drawn at random from a well-shuffl | vedclass

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

Question

(B) The total number of ways to choose $2$ cards from the same suit is given by choosing one suit out of $4$ and then choosing $2$ cards out of $13$ f

Vedclass · Accepted Answer

$\frac{2}{13}$

Vedclass · Answer

(B) The total number of ways to choose $2$ cards from the same suit is given by choosing one suit out of $4$ and then choosing $2$ cards out of $13$ from that suit. Total ways $= 4 	imes \binom{13}{2} = 4 	imes \frac{13 	imes 12}{2} = 312$. Alternatively, since the condition is that the cards are from the same suit, we consider the sample space where both cards belong to the same suit. There are $4$ suits, and for each suit, there are $\binom{13}{2} = 78$ ways to pick $2$ cards. Total outcomes $= 4 	imes 78 = 312$. In each suit, the prime-numbered cards are ${2, 3, 5, 7}$ (total $4$ cards) and the face cards are ${J, Q, K}$ (total $3$ cards). We need one face card and one prime-numbered card from the same suit. For one specific suit, the number of ways to choose one face card and one prime card is $3 	imes 4 = 12$. Since there are $4$ suits, the total number of favourable outcomes is $4 	imes (3 	imes 4) = 48$. However, the question implies the probability given that they are from the same suit. Given the cards are from the same suit, the total ways to pick $2$ cards is $\binom{13}{2} = 78$. The number of ways to pick one face card ($3$ options) and one prime card ($4$ options) is $3 	imes 4 = 12$. Since the order does not matter, we have $12$ ways. Probability $= \frac{12}{78} = \frac{2}{13}$.

$Face$	$1$	$2$	$3$	$4$	$5$	$6$
$Probability$	$0.1$	$0.32$	$0.21$	$0.15$	$0.05$	$0.17$

If $2$ cards drawn at random from a well-shuffled pack of $52$ playing cards are from the same suit, then the probability of getting a face card and a card having a prime number is

Similar Questions

Three numbers are chosen at random without replacement from $\{1, 2, 3, 4, 5, 6, 7, 8\}$. The probability that their minimum is $3$,given that their maximum is $6$,is:

An urn $A$ contains $3$ white and $5$ black balls. Another urn $B$ contains $6$ white and $8$ black balls. $A$ ball is picked from $A$ at random and then transferred to $B$. Then, a ball is picked at random from $B$. The probability that it is a white ball is

If $P(A) = \frac{1}{2}$ and $P(B) = 0$,then $P(A | B)$ is

For a biased die,the probabilities for different faces to turn up are given below:

$Face$ $1$ $2$ $3$ $4$ $5$ $6$

$Probability$ $0.1$ $0.32$ $0.21$ $0.15$ $0.05$ $0.17$

The die is tossed and you are told that either face $1$ or $2$ has turned up. Then the probability that it is face $1$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module