Question:
In 2002, the Centers for Disease Control and Prevention (CDC) reported that 8% of women married for the first time by their 18th birthday, 25% married by their 20th birthday, and 76% married by their 30th birthday. Based on these data, what is the probability that in a family with two daughters, the first and second daughter will be married by the following ages? (Enter your answers to four decimal places.) (a) 18 years of age (b) 20 years of age (c) 30 years of age
Answer:
A.) 0.0064
B.) 0.0625
C.) 0.5776
Explanation:
Given the following :
Married by 18th birthday = 8% = 0.08
Married by 20th birthday = 25% = 0.25
Married by 30th birthday = 76% = 0.76
In a family with two(2) daughters :
P(First daughter will be married by 18) = 0.08
P(second daughter will be married by 18) = 0.08
P(1st and 2nd married by 18) = (0.08×0.08) = 0.0064
B.)
P(First daughter will be married by 20) = 0.25
P(second daughter will be married by 20) = 0.25
P(1st and 2nd married by 20) = (0.25×0.25) = 0.0625
C.)
P(First daughter will be married by 30) = 0.76
P(second daughter will be married by 30) = 0.76
P(1st and 2nd married by 30) = (0.76×0.76) = 0.5776