Question

2 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is an ace? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

The answer is 0.1493.

Explanation:

In a standard deck there are 52 cards in total and there are 4 aces.

Two cards can be drawn from the 52 cards in
`^(52)C_2 = (52!)/(50!*2!) = 51*26` ways.

There are (52 - 4) = 48 cards rather than the aces.

From these 48 cards 2 cards can be drawn in
`^(48)C_2 = (48!)/(46!*2!) = 47*24` ways.

The probability of choosing 2 cards without aces is
`(47*24)/(51*26) = (188)/(221)`.

The probability of getting at least one of the cards will be an ace is
`1 - (188)/(221) = (33)/(221) = 0.1493`.