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Chapter 13: Q. 28 (page 865)

Assigning Probabilities A coin is weighted so that tails is twice as likely as heads to occur. What probability should we assign to heads? to tails?

Short Answer

Expert verified

The probability is PT=23,PH=13.

Step by step solution

01

Step 1. Given information. 

A coin is weighted so that tails is twice as likely as heads to occur. What probability should we assign to heads? to tails?

02

Step 2. Find probability. 

We are given that the tail Tis twice times as likely as heads Hto occur in a coin. Thus, we can let

PH=xPT=2x

Since the sum of the probabilities of the possible outcomes must equal 1, we have

PT+PH=1

Substituting the value of localid="1647255351165" P(T)andP(H)and solving for x ,we have

PT+PH=12x+x=13x=1x=13

Since x=13, assign the probabilities

PT=2x=23,PH=x=13.

03

Step 3. Conclusion. 

The probability is PT=23,PH=13.

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