2. In a sample survey, 1000 senior citizens were asked whether or not they have
ID: 3254922 • Letter: 2
Question
2. In a sample survey, 1000 senior citizens were asked whether or not they have ever been victimized
by a dishonest telemarketer. The table gives the responses by age group (in years).
Ages Have been victimized Have never been victimized
60-69 60 388
70-79 80 248
80 or over 34 190
Suppose one person is randomly selected from the 1000 senior citizens:
(a) Find the probability the person has been victimized and is 80 years or older.
(b) What is the probability the person has been victimized?
(c) What is the probability they have never been victimized given the person is between 60-69
years old?
(d) Find the probability the person is between 70-79 or 80 or over years old?
Explanation / Answer
a) P(the person has been victimized and is 80 years or older) = 34/1000 = 0.034
b) P(the person has been victimized) = (60 + 80 + 34) / 1000 = 0.174
c) P(they have never been victimized | person is between 60-69 years old) = P(they have never been victimized and person is between 60-69 years old) / P(person is between 60-69 years old)
= [388/1000] / [(60 + 388) / 1000]
= 388 / 448
= 0.866
d) P(person is between 70-79 or 80 or over years old) = P(person is between 70-79 years old) + P(person is between 80 or over years old)
= (80+248)/1000 + (34+190)/1000
= 0.552
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