Two cards are chosen from a standard deck of 52 playing cards without replacement. What is the probability both cards will be an Ace

(4/52)*(3/52)

To find the probability of drawing two Aces from a standard deck of 52 playing cards, we need to determine the total number of outcomes and the number of favorable outcomes.

Step 1: Calculate the total number of outcomes.
In a standard deck of 52 playing cards, there are four Aces. So, the total number of ways to choose two cards from 52 is given by the combination formula:

C(52, 2) = 52! / (2! * (52 - 2)!) = 52! / (2! * 50!) = (52 * 51) / (2 * 1) = 1326

Therefore, there are 1326 possible two-card combinations.

Step 2: Calculate the number of favorable outcomes.
In a deck of 52 playing cards, there are four Aces. When drawing two cards without replacement, we need to consider that there will only be three Aces remaining after drawing the first Ace. Therefore, the number of ways to choose two Aces is given by the combination formula:

C(4, 2) = 4! / (2! * (4 - 2)!) = 4! / (2! * 2!) = (4 * 3) / (2 * 1) = 6

So, there are 6 different combinations of drawing two Aces.

Step 3: Calculate the probability.
The probability of an event happening is given by:

Probability = Number of favorable outcomes / Total number of outcomes

Therefore, for drawing two Aces from a standard deck of 52 playing cards, the probability is:

Probability = 6 / 1326 ≈ 0.0045 (rounded to 4 decimal places)