Question

12. (12 pts) The data in the following table represent the marital status of males and females 18 years old or older in the United States in 2003.

	Males (in millions)	Females (in millions)	Totals (in millions)
Never Married	28.6	23.3	51.9
Married	62.1		124.9
Widowed	2.7	11.3
Divorced	9.0	12.7	21.7
Totals (in millions)		110.1

a) Complete the table.

b) Find the odds that a randomly selected person is a female.

c) Determine the probability that a randomly selected person was married and a female.

d) Determine the probability that a randomly selected person was widowed or a male.

e) Assuming that two people are selected independently of each other, what is the probability that both were divorced?

f) What is the probability that a randomly selected person was female if it is known that she was never married?

g) Are the events “male” and “never married” mutually exclusive (disjoint)? Explain why or why not.

h) Are the events “female” and “divorced” independent? Show work to justify your answer.

Answer 1

from above:

a)

	males	female	total
never	28.6	23.3	51.9
married	62.1	62.8	124.9
widowed	2.7	11.3	14
divorced	9	12.7	21.7
total	102.4	110.1	212.5

b)

odds that a randomly selected person is a female =110.1/102.4 =1.0752 to 1

c)

probability that a randomly selected person was married and a female =62.8/212.5=0.295529

d)

probability that a randomly selected person was widowed or a male =(14+102.4-2.7)/212.5=0.535059

e)

probability that both were divorced =(21.7/212.5)*(21.7/212.5)=0.010428

f)

probability that a randomly selected person was female if it is known that she was never married =23.3/51.9=0.448940

g)no as they contain 28.6 million people in common

h)no as P(female)*P(divorced)=(110.1/212.5)*(21.7/212.5)=0.052909 is not equal to P(ffemale and divorced)=12.7/212.5=0.059765