Patients are randomly assigned to one of the four treatment groups to cure a disease:

1) Control

2) Experimental 1

3) Experimental 2

4) Experimental 3

There are 200 patients in the trial; 20 are randomly assigned to the control group and 60 are randomly assigned to each of the experimental groups. Patients will be monitored for 6 months to see if they contract the disease.

15 % of the control patients will contract the disease in 6 months

8 % in Experimental 1 will contract the disease in 6 months

4 % in Experimental 2 will contract the disease in 6 months

1 % in Experimental 3 will contract the disease in 6 months

a) Suppose that a patient in the trial is selected at random. What is the probability that the patient contracts the disease within 6 months?

b) Suppose that a patient contracts the disease within 6 months. What is the probability that this patient was assigned to the control group?

c) Suppose that a patient does not contract the disease within 6 months. What is the probability that this patient was assigned to the Experimental 3 group?