The following table shows the results of a survey in which 102 men and 103 woman
ID: 3180287 • Letter: T
Question
The following table shows the results of a survey in which 102 men and 103 woman workers ages 25 to 64 were asked if they have at least one (1) month's income set aside for emergencies. (a) Find Pr(a worker selected at random has one month's income or more set aside for emergencies.) (b) Given that a randomly selected worker is a male, find Pr(that the worker has less than one month's income.) (c) Given that a randomly selected worker has one month's income or more, find the probability that the worker is a female. (d) Are the events of having less than one month's income or more saved and being a male independent or dependent? Explain your response.Explanation / Answer
a) P(one month's income or more) = 99 / 205 = 0.4829
b) P(less than one month's income | male) = P(less than one month's income and male) / P(male)
= (47/205) / (102/205)
= 47/102
= 0.4608
c) P(female | one month's income or more) = P(female and one month's income or more) / P(one month's income or more)
= (44/205) / (106/205)
= 44/106
= 0.4151
d) P(less than one month's income | male) = 0.4608
P(less than one month's income) = 106/205 = 0.5171
Since, P(less than one month's income | male) is not equal to P(less than one month's income) , the events are not independent events.
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