Question

Suppose that two cards are randomly selected from a standard​ 52-card deck. ​(a) what is the probability that the first card is a club and the second card is a club if the sampling is done without​ replacement? ​(b) what is the probability that the first card is a club and the second card is a club if the sampling is done with​ replacement?

Answer 1

There are 13 clubs in a standard 52 card deck. The first time you draw a club the odds of doing it are
13/52 = 1/4
The second time you draw a club, the number of clubs have gone down by 1 and the number of cards in the deck have also gone down by 1.

So this time the odds are12/51

The probability of both happening, one after the other without replacement is
1/4 * 12/51 = (1*12)/(4*51) = 12/204 = 3/51 = 1/17

1/17 = 0.0588