A standard deck of playing cards has 52 cards. There are four suits (clubs, diam

Question

A standard deck of playing cards has 52 cards. There are four suits (clubs, diamonds, hearts and spades). Each suit has 13 cards. Of the 13 cards in each suit, there are 9 numbered cards (2 through 10; an Ace (number value 1. In some games, it can be either the highest value or lowest value); a jack (eleventh in rank); a queen (12th in rank) and a king (13th in rank). Consider a game where three cards are dealt to each person. Find the probility that the player get a pair (two cards of the same numerical vaule of rank) and no higher (i.e. they do not get three cards of the same numerical value or rank). Round your answer to the nearest 0.001.

Explanation / Answer

So, first choose the pair - this can be done in 13C2 ways to choose the number and then 4C2 to choose the suit. After that, we have to choose the last card - if we had chosen pair of 2, only possibility is ace - 4C1 ways. if 3, we have 2 possibilities - A,2 - 2*4C1(4C1 is always to choose the suit. ) King also has 12 as ace can be included below too. And so on. for the ace we have 12 possibilities 2,3...Q,k So, since all the numbers come with equal probability, Here #ways = (12+12+ 11+ ...+1)/13*4C2*(13C2) / (52C3) =0.1556 Message me if you have any doubts

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