(Use Excel when providing solutions. Utilize Excel functions and formulas) 4.56

Question

(Use Excel when providing solutions. Utilize Excel functions and formulas)

4.56 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. Status Within 2 Years After Treatment Not Convicted Convicted Totals Education 10 Years or More 9 Years or Less Totals .10 27 .37 40 60 1.00 30 63 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: b. B C. AnB

Explanation / Answer

a)
P(A) = P(A|B) + P(A|B')
= 0.1 + 0.3
= 0.4

b)
P(B) = P(B|A) + P(B|A')
= 0.1 + 0.27
= 0.37

c)
P(A and B) = 0.1

Eduction B B' A 0.1 0.3 A' 0.27 0.33

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