Probability of rst marriage among women A National Center fo

Probability of rst marriage among women. A National Center for Health Statistics (NCHS) brief report by the Centers for Disease Control and Prevention (CDC) in 2009 identied that about 6% of women in the United States married for the rst time by their 18th birthday, 50% married by their 25th birthday, and 74% mar-ried by their 30th birthday. Based on these data, what is the probability that in a family with two daughters, the rst and second daughter will be married by each of the following ages?

(a) 18 years of age

(b) 25 years of age

(c) 30 years of age ]

Solution

AS THERE ARE TWO DAUGHTERS AND THE PROBABILITY OF MARRIAGE AT 18 = 0.06 , AT 25 = 0.50 AND AT 30TH = 0.75

WE HAVE TO KNW THAT IN THE QUESTION IT IS WRITTEN \"BY\" WHICH MEANS IT IS THE CUMULATIVE PROBABILITY AT EACH STAGE, LIKE MARRIAGE AT 25 INCLUDE MARRIAGE AT 18, SIMILARLY MARRIAGE BY 30 INCLUDES ALL THREE

NOW

A) P( BY 18) = 0.06^2 = 0.0036

B) P( BY 25) = 0.5^2 = 0.25

C) P( AT 30) = 0.75^2 = 0.5625