Chapter 4.6, Problem 4.56E

Drug Offenders A study of drug offenders who have been treated 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.

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. $A\cap B$

d. $A\cup B$   e. $A^c$   f. ${\left(A\cup B\right)}^c$

g. ${\left(A\cap B\right)}^c$   h. A given that B has occurredM

i. B given that A has occurred