Question
(1) (15 points) A survey about a measure to legalize medical marijuanah is taken in three states: Kentucky, Maine and Arkansas. In Kentucky, 50% of voters support the measure, in Maine, 60% of the voters support the measure, and in Arkansas, 35% of the voters support the measure. Of the total population of the three states, 40% live in Kentucky , 25% live in Maine, and 35% live in Arkansas. (a) (5 points) Given that a voter supports the measure, what is the probability that he/she lives in Maine? (b) (5 points) What is the probability that a randomly selected voter DOESN'T support the measure? (c) (5 points) What is the probability that a randomly selected voter is from Maine OR supports the measure?
Explanation / Answer
Ans:
Given that
P( support/Kentucky)=0.5
P( support/Maine)=0.6
P( support/Arkansas)=0.35
P(Kentucky)=0.4,
P(Maine)=0.25
P(Arkansas)=0.35
P(support)=0.5*0.4+0.6*0.25+0.35*0.35=0.4725
a)P(Maine/support)=P(support/Maine)*P(Maine)/P(support)
=0.6*0.25/0.4725
=0.15/0.4725
=0.3175
b)P(does not support)=1-P(support)=1-0.4725=0.5275
c)
P(Maine and support)=0.6*0.25=0.15
P(Maine or support )=P(Maine)+P(support)-P(Maine and support)
=0.25+0.4725-0.15
=0.5725