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Sum

Two cards are drawn from a pack of 52 cards. Find the probability that both are black.

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#### Solution

Two cards can be drawn from a pack of 52 cards in ^{52}C_{2} ways.

∴ n(S) = ^{52}C_{2}

Let A be the event that both the cards drawn are black.

The pack of 52 cards contains 26 black cards.

∴ 2 cards can be drawn from them in ^{26}C_{2} ways

∴ n(A) = ^{26}C_{2}

∴ P(A) = `("n"("A"))/("n"("S"))`

= `(""^26"C"_2)/(""^52"C"_2)`

Concept: Elementary Properties of Probability

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