A standard deck of 52 cards is comprised of 4 suits (Hearts, Spades, Clubs, Diam

Question

A standard deck of 52 cards is comprised of 4 suits (Hearts, Spades, Clubs, Diamonds) each containing cards of 13 ranks (2,3,4,5,6,7,8,9,10,J,Q,K,A). One pair is obtained when 2 of the cards in your hand are the same rank, and the remaining cards are all of distinct ranks.

a) Consider the scenario in which you roll a 4-sided die (with he numbers 1,2,3,4) and draw that many cards from the deck. What is the probability of getting exactly one pair?


b) Consider the scenario where you draw one card from the deck. If it is a number card of rank n, you draw n more cards from the deck (you will have n+1 cards total)/ Given that the first card is the 5 of hearts, what is the probability of getting exactly one pair?

Explanation / Answer

a) (13 combination 1)*(4 combination 2)*(12 combination 3)*(4 com 1)*(4 com 1)*(4 com 1). There are 13 different numbers. Each comes in 4 different kind. so, first you pick 1 number and then 2 from 4 possible kind. Takes care of the pair. Now, 12 different numbers remaining, pick 3 with each coming with 4 different kind.

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