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Chapter 3: Q 3.43 (page 101)

There are 3 coins in a box. One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time. When one of the 3 coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?

Short Answer

Expert verified

With the help of diagram below we get the answer as follows

13×1=13

13×12=16

13×34=14

Step by step solution

01

Given information

From the given information that there are three coins in a box. One is two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time.

One of the 3 coins is selected at random and flipped, it shows heads.

We have to find the probability that it was the two-headed coin.

02

Diagram

Let us assume that T=two-headed;

F=fair, B=biased; head.

We need to construct the following diagram is as follows:

03

Final answer

From the diagram we have

13×1=13

13×12=16

13×34=14

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