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 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: Status within Two Years after Treatment Education Convicted Not 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 1 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 two years after completion of treatment. a. Find P(A U B) b. Find P(A UB) C. Find P(B|A). d. Are the events A and B mutually exclusive? Explain. e. Are the events A and B independent? Justify your