How do you find the probability of drawing two aces without replacement?

To find the probability of drawing two aces without replacement, multiply the probabilities of each draw.

When you draw cards without replacement, the total number of cards in the deck decreases with each draw. A standard deck has 52 cards, including 4 aces.

First, calculate the probability of drawing an ace on the first draw. There are 4 aces out of 52 cards, so the probability is \( \frac{4}{52} \) or \( \frac{1}{13} \).

Next, if you successfully draw an ace, there are now 51 cards left in the deck, with only 3 aces remaining. The probability of drawing a second ace is \( \frac{3}{51} \) or \( \frac{1}{17} \).

To find the combined probability of both events happening (drawing an ace first and then another ace), you multiply the probabilities of each individual event:
\[ \frac{4}{52} \times \frac{3}{51} = \frac{1}{13} \times \frac{1}{17} = \frac{1}{221} \]

So, the probability of drawing two aces in a row without replacement is \( \frac{1}{221} \).