The probability of getting a king and a spade | vedclass

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(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

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