Two cards are drawn from a standard deck of 52 where the first card is replaced before the second card is draw

Question

1.Two cards are drawn from a standard deck of 52 where the first card is replaced before the second card is drawn. Find the probability that both cards are face cards (jack, queen, or king).

2.Two cards are drawn from a standard deck of 52 where the first card is NOT replaced before the second card is drawn. Find the probability that both cards are face cards (jack, queen, or king).

3.Two cards are drawn from a standard deck of 52 where the first card is NOT replaced before the second card is drawn. Find the probability that both cards are aces.

Answer 1

1. There are 12 possible outcomes out of 52, so the probability of drawing a face card on the first draw is 12/52 (=3/13). Since the card is replaced, the probability is the same on the second draw. Therefore, the overall probability is 3/13*3/13=9/169.

2. Again, the probability on the first draw is 12/52 (=3/13). However, in this scenario, the card is not replaced. We assume that a face card was drawn the first time, since we are finding the probability of drawing two face cards IN A ROW. That means there are now 11 face cards left in a deck that now contains 51 cards, so the probability is 11/51. Therefore, the overall probability is 3/13*11/51=33/663=11/221

3. In this scenario, the probability on the first draw is 4/52 (=1/13), and again, the card is not replaced. We assume that an ace was drawn the first time, since we are finding the probability of drawing two aces IN A ROW. That means there are now 3 aces left in a deck that now contains 51 cards, so the probability is 3/51 (=1/17). Therefore, the overall probability is 1/13*1/17=1/221.


**Note: You add the various probabilities if the outcomes are INDEPENDENT of one other. You multiply them if the outcomes are DEPENDENT on one another.**

Answer 2

None of those. I think the answer is 3/663. The probability of the first ace being drawn is 4/52, or 1/13. After that, as the first card is NOT replaced, there are 51 cards left, and 3 aces left. So the probability of the second card being an ace is 3/51. So the two probabilities combined is 1/13 * 3/51 = 3/663.

Answer 3

Chapter 12.5!!! LOL well i just learned it too. The first one would be 12/52+12/51. The second would be 12/52+12/52. The last one would be 4/52 + 4/52.

Answer 4

1. 12/52 x 12/52
2. 12/52 x 11/51
3. 4/52 x 3/51