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?

Question

Philoid · Accepted Answer

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

As there are 4 kings,

when 1 king is taken out kings left are 3 and total cards will be 51.

So, probability of drawing a king when one king has been taken out is:

Now when 2 kings taken out 2 kings are left, and 50 cards are there.

So, probability of drawing a king when two kings have been taken out is:

Now when 3 kings taken out 1 king is left, and 49 cards are there.

So, probability of drawing a king when three kings have been taken out is:

Probability that all 4 cards are king is:

∴P (E₁ Ո E₂ Ո E₃ Ո E₄) = p(E₁). P(E₂|E₁). P (E₃|E₁ Ո E2). P [E₄|(E₁ ՈE₂ Ո E₃ ՈE₄)]

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