A standard deck of 52 cards has 13 kinds of cards, with four cards of each kind, one in each of the four suits, hearts, diamonds, spades, and clubs. What is the probability that a five-card poker hand contains the ace of hearts?
closed as off-topic by quid♦, drhab, Thomas, TravisJ, Daniel Fischer Sep 22 '15 at 13:08
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Think of it as if you are the ace of hearts yourself. If $5$ cards are taken, then what is your chance to be one of them?
If you are one of $52$ persons of wich $5$ are elected, all with equal probability. Then what is your chance to be elected?
The probability of the hand NOT containing the ace of hearts is.... 51/52 x 50/51 x 49/50 x 48/49 x 47/48 = 0.9038 So the probability of the hand containing the ace of hearts is 1 - 0.903 = 0.0962