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=(4)/(52)=(1)/(13)`

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

`P_2=(3)/(51)=(1)/(17)`

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

`P_3=(2)/(50)=(1)/(25)`

- The probability to get a fourth Ace is:

`P_4=(1)/(49)`

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

`P=(1)/(13)\cdot(1)/(17)\cdot(1)/(25)\cdot(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{ \%}`