8. Emergency Savings The table shows the results of a survey in which 142 male a

Question

8. Emergency Savings The table shows the results 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 83 149 One month's income or more 7662 138 142 145 287 Less than one month's income 66 Total (a) 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. (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

Solution:-

a) The probability that a randomly selected worker has one month's income or more set aside for emergencies, given that worker is female is 0.4276.

Number of females = 145

The number of worker has one month's income or more set aside for emergencies and are female = 62

The probability that a randomly selected worker has one month's income or more set aside for emergencies, given that worker is female = 62/145 = 0.4276

b) The probability that a randomly selected worker is female, given that the worker has less than one month's income set aside for emergencies is 0.557.

Number of worker has less than one month's income = 149

Number of worker has less than one month's income and are females = 83

The probability that a randomly selected worker is female, given that the worker has less than one month's income set aside for emergencies = 83/149 = 0.557

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