A study of drug offenders who have been treated for drug abuse suggests that the chance 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 following table.   Status Within 2 Years After Treatment Education Convicted Not Convicted Totals 10 Years or More 0.11 0.19 0.30 9 Years or Less 0.29 0.41 0.70 Totals 0.40 0.60 1.00 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. (Round your answers to three decimal places.) (a) A   (b) B   (c) A ∩ B   (d) A ∪ B   (e) AC   (f) A given that B has occurred   (g) B given that A has occurred

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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A study of drug offenders who have been treated for drug abuse suggests that the chance 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 following table.
  Status Within 2
Years After Treatment
Education Convicted Not
Convicted
Totals
10 Years or More 0.11 0.19 0.30
9 Years or Less 0.29 0.41 0.70
Totals 0.40 0.60 1.00
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. (Round your answers to three decimal places.)
(a)
A
 
(b)
B
 
(c)
A ∩ B
 
(d)
A ∪ B
 
(e)
AC
 
(f)
A given that B has occurred
 
(g)
B given that A has occurred
 
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