Problem 77E

A study of the posttreatment behavior of a large number of drug abusers suggests that the likelihood of conviction within a two-year period after treatment may depend upon the offenders education. The proportions of the total number of cases falling in four education–conviction categories are shown in the following table:

Suppose that a single offender is selected from the treatment program. Define the events:

A: The offender has 10 or more years of education.

B: The offender is convicted within two years after completion of treatment.

Find the following:

a P ( A ).

b P ( B ).

c P ( A ∩ B).

d P ( A ∪ B).

h P ( A|B).

i P ( B| A).

Step 1 of 10:

Here the experiment under consideration is study of the posttreatment behaviour of drug abusers and randomly selecting a single offender.

The proportion of number of cases falling under different condition are given.

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 |

Also it is given that

A is the event that the offender has 10 or more years of education.

B is the event that the offender is convicted within two years of treatment.

Using these, we have to find the required probabilities.