The table below shows the results of a survey in which 142 men and 145 women wor

Question

The table below shows the results of a survey in which 142 men and 145 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 66 83 7662 142 145 287 Less than one month's income One month's income or more Total 149 138 (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 Thaving less than one month's income saved" and "being male independent or dependent? O Independent O Dependent

Explanation / Answer

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Answer to the question is as follows:

a. P(worker has one month' income or more set aside for emerg)
= N(worker has one month' income)/TOtal workers
= 138/287
= 0.481

b. P(worker has less than one month' income) = 149/287 = .519

c. P(female|worker has one month'income or more)
= P(is female and has one month'income or more)/P(worker has one
month' income or more)
= 62/138
=0.449

d. For this check if P(A)*P(B) = P(A & B)
So, Is P(having less than one month' income saved)*P(being male)
= P(having less than one month'income saved & being male) ?

P(having less than one month' income saved)*P(being male) = (149/287)*(142/287) = 0.257
P(having less than one month'income saved & being male) = 66/287 = 0.229965157

Since these aren't equal we conclude that the events are B. Dependent

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