Chapter 12, Problem 12.22CYS

To determine

To find: The meaning of the probability that being dealt a straight flush in a five card poker hand is $\frac{1}{64,974}$.

Answer to Problem 12.22CYS

The correct option is (a) if a person deal with millions of poker hands, the fraction of them that contain a straight flush will be too close to $\frac{1}{64,974}$

Explanation of Solution

Reason for Correct answer:

In a long run, of a large number of hands in a five-cards, the probability to get a straight flush in a five-card poker hand is $\frac{1}{64,974}$.

Reason for Incorrect answer:

Option (b) If a person deals with 64,974 poker hands, exactly one among them will contain a straight flush.

It is mentioned that the probability of picking straight flush in a five-card poker hand is $\frac{1}{64,974}$. The option tells that in a 64,974 poker hands, only one among them will have a straight flush. Thus, in a 64,974 poker hands, exactly one among them will contain a straight flush which is incorrect.

Option (c) If a person deals with 6,497,400 poker hands, exactly 100 among them will contain a straight flush.

The option tells that there 6,497,400 poker hands and 100 of them will have a straight flush which is incorrect. Thus, in a 6,497,400 poker hands, exactly 100 among them will contain a straight flush which is incorrect.

Conclusion:

Thus, if a person deals with millions of poker hands, the fraction of them that contain a straight flush will be too close to $\frac{1}{64,974}$.

Statistics Concept Introduction

Introduction:

Poker game is a card game consisting of 52 cards each card falling under one of the type Clubs, Spades, Hearts and Diamonds. A straight flush represents five consecutive cards of the same type.