Two cards are drawn from a pack of 52 cards. Find the probability that one is spade and other is non-spade. - Mathematics and Statistics

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Sum

Two cards are drawn from a pack of 52 cards. Find the probability that one is spade and other is non-spade.

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Solution

Two cards can be drawn from a pack of 52 cards in 52C2 ways.
∴ n(S) = 52C2
Let E be the event that out of the two cards drawn one is a spade and other is non-spade.
There are 13 spade cards and 39 cards are non-spade cards in a pack of 52 cards.
∴ One spade card can be drawn from 13 spade cards in 13C1 ways and one non-spade card can be drawn from 39 non-spade cards in 39C1 ways.
∴ n(E) =  13C1 × 39C1

∴ P(E) = `("n"("E"))/("n"("S")`

= `(""^13"C"_1 xx ""^39"C"_1)/(""^52"C"_2)`

Concept: Elementary Properties of Probability
  Is there an error in this question or solution?
Chapter 7: Probability - Exercise 7.2 [Page 102]

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