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Chapter 13: Q. 27 (page 865)

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

Short Answer

Expert verified

The probability isPT=15,PH=45.

Step by step solution

01

Step 1. Given information.

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

02

Step 2. Find probability.

We are given that the heads H is four times as likely as tailsTto occur in a coin. Thus, we can let

PT=xPH=4x

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

PT+PH=1

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

PT+PH=1x+4x=15x=1x=15

Since x=15, assign the probabilities

localid="1647248180167" PT=x=15,PH=4x=415=45.

03

Step 3. Conclusion.

The probability isPT=15,PH=45.

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