# Probability question

Two cards are drawn from the top of a well-shuffled deck. What is the probability that they are both black aces?

There are
52
cards in a deck, and there are
4
aces in a deck, so the probability of drawing an ace is
4
52

If you do not replace the card, there are only
51
cards left and only
3
aces left, so the probability of now drawing an ace is
3
52

# Multiply these probabilities: 4 52 x 3 51

12
2652

0.00452

but the answer is wrong.because in question it is clearly mentioned that i have to pick up the black ace.

and please tell me what is the wrong in my approach-
A =that the cards must be black
so p(A)=1/2
B=probability of getting 2 aces.
p(B/A)=probability of getting(2 aces which should be black)=2/261/25
p(A and B)=p(A)p(B/A)
=1/2
2/26
1/25
=1/650

you have picked all.so can you correct it now?

without replacement:
There are 52 cards in a deck, and there are 2 aces in a deck wit black color, so the probability of drawing an ace is 2/52.
If you do not replace the card, there are only 51 cards left and only 1 black
ace left, so the probability of now drawing an ace is 1/52.
Multily both these probablities : (2/52) * (1/52) = 0.0007396
with replacement:(2/52) * (2/52) =0.00147

[quote=“iftekar-patel-f1e6bf65, post:7, topic:3032, full:true”]
without replacement:
There are 52 cards in a deck, and there are 2 aces in a deck wit black color, so the probability of drawing an ace is 2/52.
If you do not replace the card, there are only 51 cards left and only 1 black
ace left, so the probability of now drawing an ace is 1/52.
Multily both these probablities : (2/52) * (1/51) = 0.0007541
with replacement:(2/52) * (2/52) =0.00147

but what is the wrong in above approach-Probability question.