Problem 1140

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing an ace.




The probability of an event E that is a subset of a sample space S is P(E) = \frac{n(E)}{n(S)}, where n(E) is the number of outcomes in the event and n(S) is the number of outcomes in the sample space.

The sample space is the set of all possible outcomes for drawing a single card from the deck. Since there are 52 different cards in the deck, the sample space has 52 outcomes, or n(S) = 52.

A deck of 52 cards has four suits (hearts, clubs, diamonds, and spades) with 13 cards each, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace. Hearts and diamonds are red, while clubs and spades are black. There are 4 ways to draw an ace.

ace  of hearts, ace of clubs, ace if diamonds, and ace of spades.

Therefore , there are n(E) = 4 outcomes in the event.

Divide n(E) = 4 by n(S) = 52 to write the probability.

P(E) = \frac{n(E)}{n(S)}



Therefore, the probability of drawing an ace is \frac{1}{13}.



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