Question

Determine the probability of being dealt 4 Aces of cards, from a deck of 52 playing cards, without replacement.

Answer 1

You know that the number of playing cards in the deck is 52.

Then, since you need to determine the probability of being dealt 4 Aces of cards without replacement, you need to set up the following:

- The probability to get the first Ace:

$P_1=\frac{4}{52}=\frac{1}{13}$

- You have 51 playing cards left. Then, the probability to get a second Ace is:

$P_2=\frac{3}{51}=\frac{1}{17}$

- Now you have 50 playing cards left. Then, the probability to get a third Ace is:

$P_3=\frac{2}{50}=\frac{1}{25}$

- The probability to get a fourth Ace is:

$P_4=\frac{1}{49}$

Therefore, the probability of being dealt 4 Aces of cards can be found by solving this Multiplication:

$P=\frac{1}{13}\cdot\frac{1}{17}\cdot\frac{1}{25}\cdot\frac{1}{49}$

Hence, you get:

$P\approx0.00000369$

In percent form:

$P\approx0.00000369\cdot100\approx0.000369\text{ \%}$

Hence, the answer is:

$P\approx0.000369\text{ \%}$