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# A poker hand is defined as drawing 5 cards at random

ISBN: 9780321923271 41

## Solution for problem 17E Chapter 1.2

Probability and Statistical Inference | 9th Edition

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Problem 17E

PROBLEM 17E

A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. Find the probability of each of the following poker hands:

(a) Four of a kind (four cards of equal face value and one card of a different value).

(b) Full house (one pair and one triple of cards with equal face value).

(c) Three of a kind (three equal face values plus two cards of different values).

(d) Two pairs (two pairs of equal face value plus one card of a different value).

(e) One pair (one pair of equal face value plus three cards of different values).

Step-by-Step Solution:

Step 1 of 5 :

Given, A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards.

The claim is to find the probability four of a kind ( four cards of equal face value and one card of a different value.)

The total number of ways  different poker hand can be possible  =

The number of ways when four of a kind =

=

Therefore, P(four of a kind) =

=

=

= 0.0002400.

Step 2 of 5 :

b)

the claim is to find the probability of full house ( one pair and one triple of cards with equal face value).

Full house ways = ( ways of choosing a pair) ( ways of choosing triple)

= ( )  ( )

= ( 136) (12 4)

= (78) (48)

= 3744

Therefore, P( full house ways) =

=

= 0.00144

The probability of full house ways is 0.00144

Step 3 of 5 :

c)

The claim is to find the probability three of a kind (  three equal face values plus two cards of different values).

3 of a kind = (  )

= ( 134664  4)

= 54912

Therefore, P( 3 of a kind) =

=

= 0.0211

The probability 3 of a kind is 0.0211.

Step 4 of 5

Step 5 of 5

##### ISBN: 9780321923271

Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. Since the solution to 17E from 1.2 chapter was answered, more than 272 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. The answer to “A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. Find the probability of each of the following poker hands:(a) Four of a kind (four cards of equal face value and one card of a different value).(b) Full house (one pair and one triple of cards with equal face value).(c) Three of a kind (three equal face values plus two cards of different values).(d) Two pairs (two pairs of equal face value plus one card of a different value).(e) One pair (one pair of equal face value plus three cards of different values).” is broken down into a number of easy to follow steps, and 103 words. The full step-by-step solution to problem: 17E from chapter: 1.2 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. This full solution covers the following key subjects: Cards, equal, face, pair, plus. This expansive textbook survival guide covers 59 chapters, and 1476 solutions.

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