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.

Respuesta :

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 [tex]^{52}C_2 = \frac{52!}{50!\times2!} = 51\times26[/tex] ways.

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

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

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

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