Question: Drug Offenders. A study of the behavior of a large number of drug offenders after treatment for drug abuse suggests that the likelihood of conviction within a 2-year period after treatment may depend on the offender’s education. The proportions of the total number of cases that fall into four education/conviction categories are shown in the table below.

10 Years or more .10 .30 .40

9 Years or less .27 .33 .60

Totals .37 .63 1.00

Suppose a single offender is selected from the treatment program. Here are the events of interest:

a. The offender has 10 or more years of education

b. The offender is convicted within 2 years after completion of treatment.

Find the appropriate probabilities for these events:

a. A b. B c. A n B d. A U B e. A ^c f. (A U B)^c

g. (A n B)^c h. A given that B has occurred i. B given that A has occurred.