Question

Two cards are drawn from a standard 52-card deck, without replacement. Find the probability that they are both aces.

A.
1/2652
B.
3/676
C.
1/221
D.
1/169



Please select the best answer from the choices provided

Answer 1

4 aces in a deck = 4/52 = 1/13
then without replacement, 3 aces in 51 cards
so
1/13 * 3/51
= 3/663
= 1/221

answer
C.
1/221

Answer 2

Answer: The correct option is (C)
`(1)/(221).`

Step-by-step explanation: Given that two cards are drawn from a standard 52-card deck without replacement.

We are to find the probability that both the cards are aces.

We know that there are 4 aces in a deck of 52 cards.

Let S denote the sample space for the experiment of drawing a card from a deck of 52 cards.

Then, n(S) = 52.

Let A denote the event that the first card drawn is an ace.

Then, n(A) = 4.

So, probability of event A will be

`P(A)=(n(A))/(n(S))=(4)/(52)=(1)/(13).`

Now, since the second card is drawn without replacing the first ace card, so the probability that both the cards are aces will be

`P=P(A)* (3)/(51)=(1)/(13)*(3)/(51)=(1)/(221).`

Thus, the required probability is
`(1)/(221).`

Option (C) is CORRECT.