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

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 52C2 ways.
∴ n(S) = 52C2

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 26C2 ways
∴ n(A) = 26C2

∴ P(A) = `("n"("A"))/("n"("S"))`

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

Concept: Elementary Properties of Probability
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