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1. It is estimated that 90% of those brought to trial for a crime are guilty. Of those who are guilty, 80% are convicted, 5% are acquitted and 15% have mistrials. Of those who are innocent, 5% are convicted, 75% are acquitted and 20% have mistrials.

a) Make a tree diagram for this information. Use the set of all those brought to trial as the sample space.

b) What is the probability someone who is guilty was convicted?

c) What is the probability someone who was convicted is guilty?

d) What is the probability someone brought to trial is guilty and was convicted?

2. It is estimated that 10% of people tested for use of a certain drug are actually drug users. A test for this drug use is positive in 90% of users. The test is also positive in 7% of non users.

a) Make a tree diagram for this information.

b) What is the probability that someone who gets a positive test actually uses the drug?

c) Assume successive tests are independent. If a person takes a 2^nd test and both tests are positive, what is the probability the person is a drug user?

3. Jim, Mary and Al work independently to solve a problem. From past experience it is estimated that Jim has a probability of 0.8 of solving the problem, Mary has a probability of 0.75 of solving it and Al has a 0.6 probability of solving it. Find the probability of each event.

a) Jim and Mary both solve it. ( Al might or might not)

b) Jim or Mary, possibly both, solve it.

c) Jim does not solve it but Mary and Al both do.