Problem Solving

Two cards are drawn simultaneously from a pack of cards. what is the probability at least one of them is an ace of hearts .

Assuming a standard deck (52 cards divided into 4 suits with 13 cards each), there is only one ace of hearts. When drawing two cards, there are three possible outcomes:

Something else--Ace of hearts
Ace of hearts--something else
Something else--something else

In this instance, it would actually be easier to calculate the complementary event: not drawing the ace of hearts.

On the first card, our probability of not getting the ace of hearts is 51/52. On the second card, it is 50/52.

51/52 * 50/51 = 50/52 = 25/26

WARNING: 25/26 will always be an answer choice! GMAT writers know that using the complement is a popular method, so they will use this "false" answer as a trap.

Since we used the complement, our final step is to subtract from 1: 26/26 - 25/26 = 1/26.

Bill