Question

Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. (Round your answer to four decimal places.)

Two cards of the same suit are drawn.

Answer 1

The probability of drawing, say, two clubs is:
$\frac{1}{4}\times\frac{12}{51}=0.058824$
The probabilities of drawing two hearts, two spades or two diamonds is also 0.058824 for each event. The four events are mutually exclusive, therefore the probability of drawing two cards of the same suit is:
$0.058824\times 4=0.2353$

Answer 2

There are 52 cards in a deck of cards. In the first try, the probability of getting any card is 1/52. In the second try, there are already 51 cards because there is no replacement, hence the probability on the second try is 1/51. Hence the probavility of the two events is 1/52*1/51 equal to  1/2652.