22. The table below shows the results of a survey in which 142 men and 146 women
ID: 3129274 • Letter: 2
Question
22. The table below shows the results of a survey in which 142 men and 146 women workers ages 25 to 64 were asked if they have at least one month's income set aside for emergencies. Complete parts (a) through (d).
Men
Women
Total
Less than one month's income
65
84
149
One month's income or more
77
62
139
Total
142
146
288
(a) Find the probability that a randomly selected worker has one month's income or more set aside for emergencies.
The probability is ____. (Round to the nearest thousandth as needed.)
(b) Given that a randomly selected worker is a male, find the probability that the worker has less than one month's income.
The probability is ____. (Round to the nearest thousandth as needed.)
(c) Given that a randomly selected worker has one month's income or more, find the probability that the worker is a female.
The probability is ____. (Round to the nearest thousandth as needed.)
(d) Are the events "having less than one month's income saved" and "being male" independent or dependent?
A. Dependent
B. Independent
Men
Women
Total
Less than one month's income
65
84
149
One month's income or more
77
62
139
Total
142
146
288
Explanation / Answer
a) probability that a randomly selected worker has one month's income or more = 139 / 288
= 0.48263
b) probability that a randomly selected worker has less than one month's income, given that selected worker is a male
= Probability of male worker with less than one month's income / Probability of male worker
= (65 / 288) / (149 / 288)
= 65 / 149
= 0.4362
c) probability that the worker is a female , given that selected worker has one month's income or more
= Probability of female worker with one month's income or more / Probability of worker having one month's income or more
= (62 / 288) / (139 / 288)
= 62 / 139
= 0.4460
d) P(having less than one month's income saved) = 149 / 288
P(being male ) = 142 / 288
P(having less than one month's income saved) * P(being male ) = 149 * 142 / 2882
= 0.255087
P(having less than one month's income saved and being male) = 65 / 288
= 0.22569
Since, P(having less than one month's income saved and being male) not equals to P(having less than one month's income saved) * P(being male ) , They are not independent events.
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