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

Answer:

The answer is 0.1493.

Step-by-step 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 $^{52}C_2 = \frac{52!}{50!\times2!} = 51\times26$ ways.

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

From these 48 cards 2 cards can be drawn in $^{48}C_2 = \frac{48!}{46!\times2!} = 47\times24$ ways.

The probability of choosing 2 cards without aces is $\frac{47\times24}{51\times26} = \frac{188}{221}$.

The probability of getting at least one of the cards will be an ace is $1 - \frac{188}{221} = \frac{33}{221} = 0.1493$.