question #8 interpreting concept of a survey in which 142 male and 145 female wo

Question

question #8

interpreting concept

of a survey in which 142 male and 145 female workers ages 25 to 64 were asked if they had at least one month's income set aside for emergencies Male Female Total Less than one month's income 66 83 149 One month's income or more 76 Total ne or more 76 62 138 287 142 145 (a) Find the probability that a randomly sclected worker has one month's income or more set aside for emergencies, given that the worker is female (b) Find the probability that a randomly selected worker is female, given that the worker has less than one month's income set aside for emergencies.

Explanation / Answer

Given that,

Find the probability that a randomly selected worker has one month's income or more set aside for emergencies given that the worker is female.

P(worker has one month's income or more / female) = P(worker has one month's income or more and female) / P(female)

P(worker has one month's income or more and female) = 62 / 287 = 0.2160

P(female) = 145 / 287 = 0.5052

P(worker has one month's income or more / female) = 0.2160 / 0.5052 = 0.4276

Find the probability that a randomly selected worker is female give that the worker has less than one month's income set aside for emergencies.

P(female / worker has less than one month's income ) = P(female and worker has less than one month's income ) = P(worker has less than one month's income)

P(female) = 145/287 = 0.5052

P(female and worker has less than one month's income) = 83 / 287 = 0.2892

P(female / worker has less than one month's income ) = 0.2892 / 0.5052 = 0.5724

Male female total less than one month's income 66 83 149 one month's income or more 76 62 138 total 142 145 287

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