(1) (15 points) A survey about a measure to legalize medical marijuanah is taken

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

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