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Chapter 13: Q. 30 (page 865)

Assigning Probabilities A die is weighted so that a six cannot appear. The other faces occur with the same probability. What probability should we assign to each face?

Short Answer

Expert verified

The probability isP1=P2=P3=P4=P5=15.

Step by step solution

01

Step 1. Given information. 

A die is weighted so that a six cannot appear. The other faces occur with the same probability. What probability should we assign to each face?

02

Step 2. Find probability.  

We are given that, the six cannot appear and the other numbers in a die has the same probability. Since the sample space of a die is

S=1,2,3,4,5

Thus, we can let

P6=0P1=P2=P3=P4=P5=x

Since the sum of the probabilities of the possible outcomes must equal 1.

P1+P2+P3+P4+P5+P6=1

Substituting the given, and solving for x, we have

P1+P2+P3+P4+P5+P6=1x+x+x+x+x+0=15x=1x=15

03

Step 3. Substitute the value. 

Since x=15assign the probabilities

P1=P2=P3=P4=P5=x=15.

04

Step 4. Conclusion.

The probability isP1=P2=P3=P4=P5=15

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IfnA=15,nB=20,nA鈭�B=10. findnA鈭�B.

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