4.54 Drug Offenders A study of the behaviour of a large number of drug offenders after treatment for drug abuse suggests that the likelihood of conviction within a two-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 treat- ment 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

d. AUB g. (ANB)

b. B

e. Ac

c. ANB

f. (AUB) h. A given that B has occurred i. B given that A has occurred

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Not Education Convicted Status within Two Years after Treatment Convicted Total 10 years or more 0.10 0.30 0.40 9 years or less 0.27 0.33 0.60 Total 0.37 0.63 1.00