Problem of the Week

Problem B

Honesty - the Best Policy?

A reporter is doing interviews at a convention attended by 500 people.

• 40% of these people always tell the truth.

• 20 of them will always lie.

• The remaining people each sometimes tell the truth and sometimes lie.

1. Suppose that she interviews a person at random.

   1. As a fraction, what is the probability that the person always lies?

   2. As a fraction, what is the probability that the person always tells the truth?

2. Suppose she interviews Joe Public, a person at the convention. The last time she interviewed him, he only told her the truth, so she knows he must be a person who always tells the truth or a person who sometimes tells the truth and sometimes lies. What is the probability that Joe Public always tells the truth?

Theme: Data Management