Question

If two men took one card each (i.e., both of them together took 2 cards) from a deck of 52 cards. After they took the cards and saw it, they replaced and reshuffled the cards. Then, the two repeated the same process again. Find the probability of getting a different card the second time which is not the same as the first time for each individual?

Answer 1

The probability that the first man does not draw his card the second time around is 51/52.

Then (if the first man did not draw the second man's first card), the probability that the second man does not draw his card is 50/51.

The probability that the two men did not draw their cards is then 51/52 X 50/51 = 2550/2652

But...It is also possible that the first man drew the second man's first card on his second draw. The probability for this scenario is 1/52 and then the probability that the second man does not draw his first card the second time around is 51/51 (because it is not there!)

The total probability then is 2550/2652 + 1/52 X 51/51 = 2550/2652 + 51/2652 = 2601/2652

which is approximately: .98