Question

Please help. 15 points! Two cards are randomly chosen, one at time, from a standard deck of 52 playing cards without replacement. What is the probability both cards will be an Ace?

Answer 1

-- For the first draw, there are 52 cards in the deck and 4 of them are aces.
The probability of drawing an ace is (4/52) = 1/13 .

If that draw is successful, then . . .

-- For the second draw, there are 51 cards in the deck and 3 of them are aces.
The probability of drawing an ace is (3/51) = 1/17 .

-- The probability of BOTH of these events happening is

(1/13)·(1/17) = (1/221) = 0.004525...

That's about 0.45 percent.  You should not bet money on it.

Answer 2

$|\Omega|=52\cdot51=2652\\ |A|=4\cdot3=12\\\\ P(A)=\dfrac{12}{2652}=\dfrac{1}{221}\approx0.5\%$