Two cards are drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that they are both aces if the first card is not replaced?

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Two cards are drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that they are both aces if the first card is not replaced?

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Answer 1 · 2018-03-20T16:14:19

$0.00452$ $0.00452$

-OR-

$0.452 %$ $0.452%$

Explanation:

There are $52$ $52$ cards in a deck, and there are $4$ $4$ aces in a deck, so the probability of drawing an ace is $\frac{4}{52}$ $4/52$

If you do not replace the card, there are only $51$ $51$ cards left and only $3$ $3$ aces left, so the probability of now drawing an ace is $\frac{3}{52}$ $3/52$

Multiply these probabilities:
$\frac{4}{52}$ $4/52$ x $\frac{3}{51}$ $3/51$ $=$ $=$ $\frac{12}{2652}$ $12/2652$ $\to$ $->$ $0.00452$ $0.00452$

Answer 2 · 2018-03-20T17:35:20

$\frac{1}{169}$ $1/169$

Explanation:

The probability that the first card is an ace is $\frac{4}{52} = \frac{1}{13}$ $4/52=1/13$ . The probability that the second card is an ace is $\frac{4}{52} = \frac{1}{13}$ $4/52=1/13$ .

Therefore, the probability that both cards are aces is $\frac{1}{13} \cdot \frac{1}{13} = \frac{1}{169}$ $1/13*1/13=1/169$ .

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Two cards are drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that they are both aces if the first card is not replaced?

2 Answers

Explanation:

Explanation:

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