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Chapter 5: Q R5.4. (page 334)

Weird dice Nonstandard dice can produce interesting distributions of outcomes. Suppose you have two balanced, six-sided dice. Die A has faces with 2,2,2,2,6, and6 spots. Die B has three faces with 5 spots and three faces with 1 spot. Imagine that you roll both dice at the same time.

(a) Find a probability model for the difference (Die A 鈭� Die B) in the total number of spots on the up-faces.

(b) Which die is more likely to roll a higher number? Justify your answer.

  • Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.

Short Answer

Expert verified

Part (a) Probability distribution isDProbability-313112516

Part (b) Die A can take higher values in comparison of the die B.

Step by step solution

01

Part (a) Step 1. Given Information

Die A takes the values2 and 6, whereas Die B takes the values 5 and 1

02

Part (a) Step 2. Concept

Probability=FavorableoutcomesTotaloutcomes

03

Part (a) Step 3. Calculation

The difference can be determined using the following formula:

2鈭�5=鈭�32鈭�1=6鈭�5=16鈭�1=5

The probabilities could be estimated in the following way:

P(2,5)=46脳36=13P(2,1)=46脳36=13P(6,5)=26脳36=16P(6,1)=26脳36=16

As a result, the probability distribution is as follows:

DProbability-313112516

04

Part (b) Step 3. Explanation

Die A could take the values 2 and 6based on the information supplied, whereas Die B may take the values 5 and 1. As a result, it's possible to say that die A can take higher values than die B.

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