Questions 19 and 20 refer to the following information: A Department store has b

Question

Questions 19 and 20 refer to the following information: A Department store has been the target of many shoplifters during the past month. Police investigations show that 50 percent of all caught shoplifters were first-time offenders, 70% were male and 39 percent were first-time offenders and male.

Question 19 What is the probability that a caught shoplifter is a first-time offender or male?

(a) 0.39

(b) 0.81

(c) 0.35

(d) 0.325

Question 20 What is the probability than a caught shoplifter is not a first-time offender, given that the shoplifter is female?

(a) 0.30

(b) 0.63

(c) 0.38

(d) 0.19

Explanation / Answer

Ans:

P(first time offender)=0.5

P(not first time offender)=1-0.5=0.5

P(male)=0.7

P(female)=1-0.7=0.3

P(first time offender and male)=0.39

Joint distribution:

19)P(first time offender or male)=P(first time offender)+P(male)-P(first time offender and male)

                                                    =0.5+0.7-0.39

                                                    =1.2-0.39=0.81

P(first time offender or male)=0.81

Option b is correct.

20)P(not first time offender/female)=P(not first time offender and female)/P(female)

Now,

P(not first time offender and female)=0.19

P(female)=0.3

Hence,

P(not first time offender/female)=0.19/0.3=0.63

Option b is correct.

first time offender not first time offender Total male 0.39 0.31 0.7 female 0.11 0.19 0.3 Total 0.5 0.5 1

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