The probability of getting a king and a spade | vedclass

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

Question

(D) Total number of ways to draw $2$ cards from $52$ cards is given by $n(S) = ^{52}C_2 = \frac{52 	imes 51}{2} = 1326$.
We need to find the probabi

Vedclass · Accepted Answer

$\frac{5}{442}$

Vedclass · Answer

(D) Total number of ways to draw $2$ cards from $52$ cards is given by $n(S) = ^{52}C_2 = \frac{52 	imes 51}{2} = 1326$.
We need to find the probability of getting a king and a spade card.
There is only one card that is both a king and a spade (the King of Spades).
The other card can be any of the remaining $51$ cards.
However, the question asks for the probability of getting a king and a spade card simultaneously.
This means we need to select the King of Spades and one other card such that the set contains at least one king and at least one spade.
The favorable outcomes are: (King of Spades, any other King) or (King of Spades, any other Spade).
Number of other Kings = $3$. Number of other Spades = $12$.
Total favorable outcomes = $3 + 12 = 15$.
Probability = $\frac{15}{1326} = \frac{5}{442}$.

The probability of getting a king and a spade card when two cards are drawn simultaneously from a pack of $52$ playing cards is

Similar Questions

From a well-shuffled deck of $52$ cards,$13$ cards are selected at random. The probability that the selected $13$ cards contain exactly $4$ kings is ....

Three numbers are chosen at random without replacement from $\{1, 2, \ldots, 10\}$. The probability that the minimum of the chosen numbers is $3$ or their maximum is $7$ is:

Three distinct numbers are selected from the first $100$ natural numbers. The probability that all three numbers are divisible by both $2$ and $3$ is:

If three cards are drawn randomly from a pack of $52$ playing cards, then the probability of getting exactly one spade card, exactly one king, and exactly one card having a prime number is

$A$ committee of $5$ members is to be formed from $6$ men and $4$ women. What is the probability that the committee contains at least one woman?

Vedclass Test Series

Exam Paper Generator

Online Exam Module