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in how many ways can 4 cards be selected from a pack of 52 cards such that at-least one card of heart is selected ?
 Sep 28, 2013
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The probability of getting at least one heart is the compliment of getting no hearts.
What I mean is, you either get a heart or you don't so the sum of these 2 probabilities is 1.
All probabilities are between 0 and 1 (0 = can't happen) (1 = must happen)

The probability that the first chosen is not a heart is 48/52
now there are only 51 cards left and only 47 of them are not hearts so
The probability that the second chosen is not a heart is 47/51 etc
So
The probability that none are hearts is

P(no hearts) = 1 - [ 48/52 * 47/51 * 46/50 * 45/49 ]

I hope that you LEARN from my answer.
 Sep 29, 2013

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