Use the probabilities of Exercise 4.56 to show that these equalities are true:...

Use the probabilities of Exercise 4.56 to show that these equalities are true:

Reference:

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: