Maharashtra State BoardHSC Science (Electronics) 11th
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Two cards are drawn from a pack of 52 cards. Find the probability that both are from the same suit. - Mathematics and Statistics

Sum

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

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Solution

Two cards can be drawn from a pack of 52 cards in 52C2 ways.

∴ n(S) = 52C2 

Let event  C: Both the cards are drawn are of the same suit.

A pack of 52 cards consists of 4 suits each containing 13 cards.

∴ 2 cards can be drawn from the same suit in 13C2 ways.

∴ n(C) = 13C2 × 4

∴ P(C) = `("n"("C"))/("n"("S"))`

= `(4 xx ""^13"C"_2)/(""^52"C"_2)`

= `(4 xx 13 xx 12)/(52 xx 51)`

= `4/17`

Concept: Concept of Probability
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