What is the probability that you draw 3 cards and you selected 3 aces from a deck of 52 cards?

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What is the probability that you draw 3 cards and you selected 3 aces from a deck of 52 cards?

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Answer 1 · 2017-01-23T10:17:07

$\frac{1}{11050} ≅ 9 \times 10^{- 5}$ $1/11050~=9 xx 10^(-5)$

Explanation:

There are 4 aces in a standard deck of 52 cards.

If we draw a single card, the chance we get an ace is:

$\frac{4}{52}$ $4/52$

Now let's draw a second card. We've already pulled one ace, so there are 3 left, and there are now 51 cards left, so the chance of pulling 2 aces on 2 draws is:

$\frac{4}{52} \times \frac{3}{51}$ $4/52 xx 3/51$

And following this same logic with the third draw to get a third ace, we have:

$\frac{4}{52} \times \frac{3}{51} \times \frac{2}{50} = \frac{12}{132600} = \frac{1}{11050} ≅ 9 \times 10^{- 5}$ $4/52 xx 3/51 xx 2/50=12/132600=1/11050~=9 xx 10^(-5)$

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What is the probability that you draw 3 cards and you selected 3 aces from a deck of 52 cards?

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