three cards are randomly drawn without replacement from a standard deck of 52 cards. What is the probability of drawing an ace on the third draw?

There are 4 aces in a deck of 52 cards. The probability of an ace being in any position in the deck is 4/52 = 1/13.

The probability of an ace being in the 3rd position is 1/13

To calculate the probability of drawing an ace on the third draw, we need to consider the number of favorable outcomes (drawing an ace on the third draw) and the total number of possible outcomes.

First, let's figure out the total number of possible outcomes. In the first draw, we have all 52 cards to choose from. After the first card is drawn, for the second draw, there will be 51 cards remaining, and for the third draw, there will be 50 cards left. So the total number of possible outcomes is:

52 (choices for the first draw) * 51 (choices for the second draw) * 50 (choices for the third draw) = 132,600

Next, we need to determine the number of favorable outcomes, which in this case is drawing an ace on the third draw. There are four aces in a deck of 52 cards. Since we are drawing without replacement, the probability of drawing an ace on the third draw is:

4 (aces in the deck) * 48 (non-ace cards left after the first two draws) = 192

Finally, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 192 / 132,600
Probability ≈ 0.00145 or 0.145%

Therefore, the probability of drawing an ace on the third draw is approximately 0.145%.