Question

Two cards are drawn without replacement from a pack of 52 cards. Find the probability that both are kings.

Answer 1

Total number of all favorable cases is n(S) = 52

Let A be the event that first card drawn is a king. There are four kings in the pack. Hence, the probability of the first card is a king is

P(A) = \(\cfrac4{52}\)

Let B be the event that second card is also king without replacement. Then there are 3 kings left in the pack as the cards are not replaced. Therefore, the probability of the second card is also king is

P(B|A) = \(\cfrac3{51}\)

Then the probability of getting two kings without replacement is

= P(A)P(B|A)

⇒ \(\cfrac{4}{52}\times\cfrac{1}{17}=\cfrac{1}{221}\)

The probability that both of them are kings is \(\cfrac{1}{221}\)