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 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 at the bottom of the page. The 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 requested in Parts

(a) and (b).
(Hint: Use a pair of random digits to simulate one pair of subjects. Let the first digit represent Treatment 1 and use 1– 7 as an indication of a success and 8, 9, and 0 to indicate a failure. Let the second digit represent Treatment 2, with 1– 4 representing a success. For example, if the two digits selected to represent a pair were 8 and 3, you would record failure for Treatment 1 and success for Treatment