Question

671 registered voters were randomly selected and asked about their political affiliation and whether or not they favor a national health policy for the United States. The results of this survey are reported in the table below.

Contingency Table

Position on National Health Care	Democrat (D)	Independent (I)	Republican (R)	Total
Favor (F)	161	40	130	331
Do not Favor (F')	110	40	190	340
Total	271	80	320	671

The Joint Probability Distribution or Relative Frequency Table

Position on National Health Care	Democrat (D)	Independent (I)	Republican (R)	Total
Favor (F)	0.2399	0.0596	0.1937	0.4933
Do not Favor (F')	0.1639	0.0596	0.2832	0.5067
Total	0.4039	0.1192	0.4769	1.0000

If one of the voters is randomly selected, answer the following questions.

1. What is the probability that the voter will be a Republican?
2. What is the probability that the voter will not favor a national healthcare policy?
3. What is the probability that the voter will be a Democrat and in favor of national healthcare policy?
4. Given that a voter is a Republican, what is the probability that the voter will favor a national healthcare policy?

Answer 1

From the provided contingency table:

a) the probability that the voter will be a Republican is P(R)=0.4769

b) the probability that the voter will not favor a national healthcare policy P(F')=0.5067

c) the probability that the voter will be a Democrat and in favor of national healthcare policy is P(D & F)=0.2399

d) Given that a voter is a Republican, the probability that the voter will favor a national healthcare policy is given by: