Question

In a survey of 2000 adults 50 years and older of whom 60% were retired and 40% were pre-retired, the following question was asked: Do you expect your income needs to vary from year to year in retirement? Of those who were retired, 45% answered no, and 55% answered yes. Of those who were pre-retired, 38% answered no, and 62% answered yes. If a respondent in the survey was selected at random and had answered yes to the question, what is the probability that he or she was retired? (Round your answer to three decimal places).

Answer 1

                                 Retired                     Pre-retired              Total

Yes                           0.33 0.248                 0.578

No                          0.60X0.45 = 0.27         0.40X0.38=0.152    0.422

Total                             0.60                               0.40                 1.00

P(Retired/Yes) = P(Retired & Yes)/P(Yes) = 0.33/0.578 = 0.571

So,

Answer is:

0.571