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?

-- 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.