A standard deck of playing cards consists of 4 suits: Spades, Hearts, Diamonds and Clubs. You can see them, in Word for example, by using 2660 Alt+X, 2665 Alt+X, 2666 Alt+X and 2663 Alt+X respectively. Cards sharing one of these symbols are said to be in the same suit.
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The first card can be anything. That means that there are 51 cards left and 39 of them are not the same suit as the first one, therefore P(not same suit) = 39/51 = 13/17.
1/13
If 2 cards are selected from a standard deck of 52 cards without replacement, in order to find the probability that both are the same suit, start with the first card...The probability that the first card is any suit is 52 in 52, or 1.Now, consider the second card. There are 12 cards remaining in the same suit, and 39 cards remaining in the other three suits...The probability that the second card is the same suit as the first card is 12 in 51, or 4 in 17, or 0.235.The probability of both events occurring is the product of those two probabilities. That is still 4 in 17, or 0.235.
The minimum number of cards that must be dealt, from an arbitrarily shuffled deck of 52 cards, to guarantee that three cards are from some same suit is 9.The basis for 9 is that the first four cards could be from four different suits, the next four cards could be from four different suits, and the ninth card is guaranteed to match the suit of two of the previously dealt cards. The minimum number, without the guarantee, is 3, but the probability of that is only 0.052, or about 1 in 20.
5. Assuming the first four are all different suits, the 5th card must be a duplicate suit. If any prior to the 5th card is not a new suit, it is garunteed to be a duplicate of a prior suit.