If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities.
a. Both are of the same suit.
b. Both are kings.
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No matter what the first card is, it will always be in a suit. Then for the second card, there are 51 cards left and only 12 of them are the same suit as the first one.
The probability of the first card being a king is 4/52. The probability of the second being a king are 3/51 (there is one less card and one less king.
The probability of both being a king is (4/52)×(3/51)
the first question is asking for the same suit, therefore it is 13/52 x 12/51
But it doesn't say the specific suit. If it said "both are diamonds" then it would be (13/52)×(12/51). But the first card can be anything as long as the second card is the same suit.