Question

Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings?

Answer 1

Let E₁, E₂, E₃ and E₄ be the events that first, second, third and fourth card is King respectively.

∴ P(E₁ ∩ E₂ ∩ E₃ ∩ E₄)

= `"P"("E"_1) * "P"("E"_2/"E"_1) . "P"["E"_3/(("E"_1 ∩ "E"_2))] * "P"["E"_4/(("E"_1 ∩ "E"_2 ∩ "E"_3 ∩ "E"_4))]`

= `4/52 xx 3/51 xx 2/50 xx 1/49`

= `24/(52*51*50*49)`

= `1/(13*17*25*49)`

= `1/27075`

Hence, the required probability is `1/27075`.