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4.41 Married women:  The American Community Survey estimates that 47.1% of women ages 15 years and over are married.[US Census Bureau]

(a) We randomly select three women between these ages. What is the probability that the third woman selected is the only one who is married?
(please round to four decimal places)

(b) What is the probability that all three randomly selected women are married?
(please round to four decimal places)

(c) On average, how many women would you expect to sample before selecting a married woman? What is the standard deviation? (please round both answers to two decimal places)
The expected number is , while the standard deviation is .

(d) If the proportion of married women was actually 30%, how many women would you expect to sample before selecting a married woman? What is the standard deviation? (please round both answers to two decimal places)
The expected number is now , while the standard deviation is .