The 2010 American Community Survey estimates that 47.1% of women ages 15 years and over are married.

(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?

(b) What is the probability that all three randomly selected women are married?

(c) On average, how many women would you expect to sample before selecting a married woman? What is the standard deviation?

(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?

Make sure to clearly define the random variables and specify their probability distributions and parameters.

Use R for computations in the following questions and submit your R file as well.