Chapter 12, Problem 12.22CYS

To determine

To identify: The correct option for the given study.

Answer to Problem 12.22CYS

Option (a), “If you deal thousands of poker hands, the fraction of them that contain two pairs will be very close to $\underset{\_}{\frac{1}{21}}$”.

Explanation of Solution

Reason for the correct answer:

The idea of probability is to predict the chance of happening event in the long run. The happening of an event is quite unpredictable, though the event follows a design or system of prediction.

The value $\frac{1}{21}$ defines the chance of predicting two pairs in a long run of five cards poker, or the fraction value that is close to the happening of two pairs in a long run of five cards poker.

This statement conforms to the basic idea of probability. Thus, option (a) is correct.

Reason for the incorrect answers:

The other options talk about the fraction value and defining the fraction value in terms of poker game, rather than defining the fraction value in terms of prediction (or probability).

Options (b) says that the value $\frac{1}{21}$ defines that the happening of exactly one pair in 21 poker hands, which is disagreeable to the ideology of probability.

Option (c) says that the value $\frac{1}{21}$ defines that the happening of exactly 1000 pair in 21,000 poker hands which is also disagreeable to the ideology of probability and quite similar with the last option.

The ideology of probability works on the predicting estimated value of happening event in long run, which is not capable of stating the exact outcome. Both options (b) and (c) attempt to state the exact outcome.

Thus, the options (b) and (c) are incorrect.

Conclusion:

Thus, the correct response in the study is, (a) ‘If you deal thousands of poker hands, the fraction of them that contain two pairs will be very close to $\frac{1}{21}$’.

Statistics Concept Introduction

Introduction:

The idea of Probability:

The idea of probability is to predict the chance of happening event in the long run. The happening of an event is quite unpredictable, though the event follows a design or system of prediction.