Maharashtra State BoardHSC Science (General) 11th
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Three cards are drawn from a pack of 52 cards. Find the chance that at least one is a diamond card - Mathematics and Statistics

Sum

Three cards are drawn from a pack of 52 cards. Find the chance that at least one is a diamond card

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Solution

3 cards can be drawn from a pack of 52 cards in 52C3 ways.

∴ n(S) = 52C3

Let event B: Out of the three cards drawn, at least one is a diamond.

∴ B' is the event that all 3 cards drawn are non-diamond cards.

In a pack of 52 cards, there are 39 non-diamond cards.

∴ 3 non-diamond cards can be drawn in 39C3 ways

∴ n(B') = 39C3

∴ P(B') = `("n"("B'"))/("n"("S"))`

= `(""^39"C"_3)/(""^52"C"_3)`

= `(39 xx 38 xx 37)/(52 xx 51 xx 50)`

= `703/1700`

∴ P(B) = 1 – P(B')

= `1 - 703/1700`

= `997/1700`

Concept: Concept of Probability
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