Example 1.2-10 The number of possible 13-card hands that can be selected from a

Question

Example 1.2-10 The number of possible 13-card hands that can be selected from a deck of 52 playing cards is Example1.2-11 Assume that each of the five-card hands drawn from a deck of 52 playing cards has the same probability of being selected. Then the number of possible 5-card hands that are all spades (Event A) is Think how to make the event A happen, that is how many ways that the event A can happen? How many ways we can select an all-spade five-card hand Suppose that the event B is the set of outcomes in which exactly three cards are kings and exactly two cards are queens. The number of outcomes in B is is How many ways we can select the three kings How many ways we can select the two queens Let C be the set of outcomes in which there are exactly two kings, two queens, and one jack. The number of outcomes in C is , P(C)- The probability of an all-spade five-card hand is The probability of the event B

Explanation / Answer

#1.
13 cards from a deck of 52 can be drawn in 32C13 = 635,013,559,600

#2.
Possible number of 5 spade cards = 13C5 = 1,287
5 cards selected are spade = 13C5/52C5 = 0.0005

3 Kings can be selected in 4C3 = 4 ways
2 queens can be selected in 4C2 = 6 ways

number of outcomes = 4C2*4C2*4C1 = 6*6*1 = 36
P(C) = 36/52C5 = 0.0000139

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