A woman and a man (unrelated) each has two children.
At least one of the woman’s children is a boy, and the man’s older child is a boy. Is the probability that the woman has two boys greater than, equal to, or less than the probability that the man has two boys?
a. Demonstrate the truth of your answer by using a simple sample to represent each family.
b. Demonstrate the truth of your answer by taking two samples, one from men with two children families and one from women with two-children families.
c. Demonstrate the truth of your answer using computer simulation. Using the Bernoulli probability function with p = 0.5 (let 0 = girl and 1 = boy ), generate 500 “families of two children” for the man and the woman. Determine which of the 500 satisfy the condition for each and determine the observed proportion with two boys.
d. Demonstrate the truth of your answer by repeating the computer simulation several times. Repeat the simulation in part c several times.
e. Do the preceding procedures seem to yield the same results? Explain.