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Solnce55 [7]
3 years ago
8

2 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is an a

ce? Express your answer as a fraction or a decimal number rounded to four decimal places.
Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
6 0

Answer:

<h2>The answer is 0.1493.</h2>

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.

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