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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?
Solution
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`.
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