# Four cards are drawn from a pack of 52 cards. Find the probability that at least one heart. - Mathematics and Statistics

Sum

Four cards are drawn from a pack of 52 cards. Find the probability that at least one heart.

#### Solution

4 cards can be drawn out of 52 cards in 52C4 ways.
∴ n(S) = 52C
Let C be the event that out of the four cards drawn at least one is a heart.
∴ C′ is the event that all 4 cards drawn are non-heart cards.
In a pack of 52 cards, there are 39 non-heart cards.
∴ 4 non-heart cards can be drawn in 39C4 ways.
∴ n(C′) =  39C4

∴ P(C′) = ("n"("C'"))/("n"("S") = (""^39"C"_4)/ (""^52"C"_4)
∴ P(C) =  1 – P(C') = 1 - (""^39"C"_4)/(""^52"C"_4)

Concept: Elementary Properties of Probability
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