Parts a-c (19 pts) Of the voters in a city, 40% are Republicans and 60% are Demo
ID: 2935237 • Letter: P
Question
Parts a-c
(19 pts) Of the voters in a city, 40% are Republicans and 60% are Democrats. Among the Republicans 70% are in favor of a bond issue, whereas 80% of the Democrats favor the issue. 10. (a) (6 pts) What is the probability that a randomly chosen voter is a Republican or is in favor of the bond issue? (b) (6 pts) If a voter is selected at random in the city, what is the probability that he or she will favor the bond issue? (e) (7 pts) If a voter is in favor of the bond issue, what is the probability that he or she is a Democrat?Explanation / Answer
Ans:
R=Republican;D=Democrat,F=Favor
P(R)=0.4
P(D)=0.6
P(F/R)=0.7
P(F/D)=0.8
P(F)=0.7*0.4+0.8*0.6=0.28+0.48=0.76
a)
P(F/R)=0.7=P(F and R)/P(R)
P(F and R)=0.7*0.4=0.28
P(F or R)=P(F)+P(R)-P(F and R)
=0.76+0.4-0.28
=0.88
b)P(F)=0.7*0.4+0.8*0.6=0.28+0.48=0.76
c)P(D/F)=P(F/D)*P(D)/P(F)
=0.8*0.6/0.76
=0.48/0.76
=0.6316