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

Solution:-

a)Probability that a mother in the study smoked during the pregnancy is given as

=(no. of mother smoked during the pregnancy.)/(total no. of mothers.

=1124/4329

=0.2596

b)Probability that a mother smoked during the pregnancy if her education was below high school is given by

=(The no. Of mother smoked during the pregnancy if her education was below high school)/total no. of mothers

=415/4329

=0.09586

c)Probability that a mother smoked during pregnancy and had a college degree is given by

=(the no. of mother smoked during pregnancy and had a college degree.)/total no.of mothers

=48/4329

=0.011088

d)Probability that a mother smoked during pregnancy or that she graduated from college is given by

=[(The no.of mother smoked during pregnancy)/total no. of mothers] + [(the no. of mothers graduated from college)/total no. of mothers

=(1124/4329)+(578/4329)

=0.39316

e) P= Probability ​​​​​​ that a mother did not smoke during her pregnancy given that she attended some college but did not have a degree is given by

Now, first We have to find,

P1= Probability that a mother did not smoke during her pregnancy and she attended some college but did not have a degree.

=(The no.of mother did not smoke during her pregnancy and that she attended some college but did not have a degree)/ total no. of mothers.

=635/4329

=0.146685

&

P2= Probability of mothers attended some college but did not have a degree is given by

=(the no.of mothers  attended some college but did not have a degree)/total no. of mothers

=766/4329

=0.176946

Hence,

P=P1/P2

P= 0.828981

f)Probability that a mother with some college smoked during pregnancy is given by

=(The no.of mother with some college smoked during pregnancy.)/total no. of mothers

=131/4329

=0.030261