6.82 A medical research team wishes to evaluate two different treatments for a disease. Subjects are selected two at a time, and then one of the pair is assigned to each of the two treatments. The treatments are applied, and each is either a success (S) or a failure (F).

The researchers keep track of the total number of successes for each treatment. They plan to continue the chance experiment until the number of successes for one treatment exceeds the number of successes for the other treatment by 2. For example, they might observe the results in the table for Exercise 6.82 given below. The chance experiment would stop after the sixth pair, because Treatment 1 has two more successes than Treatment 2. The researchers would conclude that Treatment 1 is preferable to Treatment 2.

Suppose that Treatment 1 has a success rate of .7

(that is, P(success) 5 .7 for Treatment 1) and that Treatment 2 has a success rate of .4. Use simulation to estimate the probabilities in Parts

(a) and

(b) by using the following procedure: