Question

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

Answer 1

Answer:  The correct option is (C) $\dfrac{1}{221}.$

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

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{4}{52}=\dfrac{1}{13}.$

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

$P=P(A)\times \dfrac{3}{51}=\dfrac{1}{13}\times\dfrac{3}{51}=\dfrac{1}{221}.$

Thus, the required probability is $\dfrac{1}{221}.$

Option (C) is CORRECT.

Answer 2

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