Question

1. Calculate the probabilities below using the following contingency table.

Mother's Education	Smoked during Pregnancy	Didn't Smoke during Pregnancy	Row     Total
Below High School	415	670	1,085
High School	530	1,370	1,900
Some College	131	635	766
College Degree	48	530	578
Column Total	1,124	3,205	4,329

1. Probability that a mother in the study smoked during the pregnancy.
2. Probability that a mother smoked during the pregnancy if her education was below high school.
3. Probability that a mother smoked during pregnancy and had a college degree.
4. Probability that a mother smoked during pregnancy or that she graduated from college.
5. Probability that a mother did not smoke during her pregnancy given that she attended some college but did not have a degree.
6. Probability that a mother with some college smoked during pregnancy.

Answer 1

(a)

Out of 4329, 1124 smoked during pregnancy so the probability that a mother in the study smoked during the pregnancy is

P( smoked during the pregnancy) = 1124 / 4329 = 0.2596

(b)

Out of 1085 women with education below high school, 415 smoked during pregnancy is

P(smoked during pregnancy | below high school) = 415 / 1085 = 0.3825

(c)

P(smoked during pregnancy and had a college degree) = 48 /4329 = 0.0111

(d)

P(smoked during the pregnancy) = 1124 / 4329 = 0.2596

P(College Degree) = 578 / 4329 = 0.1335

P(smoked during pregnancy and had a college degree) = 48 /4329 = 0.0111

P(smoked during the pregnancy or College Degree) = P(smoked during the pregnancy) + P(college degree) - P(smoked during pregnancy and had a college degree) = 0.2596 + 0.1335 - 0.0111 = 0.3820

(e)

P(did not smoke | some college) = 635 / 766 = 0.8290

(f)

P(smoke | some college) = 131 / 766 = 0.1710