Suppose that in a certain country there are only two political parties, Dingos (

Question

Suppose that in a certain country there are only two political parties, Dingos (D) and Reptiles (R). In a particular town, 65% of the voters favor R, 20% of the voters favor D, and 15% of the voters have no strong preference for either. Suppose that 82% of the D supporters voted for their candidate (Binton) and 18% of the D voted for the R candidate (Clush). Suppose that 72% of the R voted for Clush and 28% of the R supporters voted for Binton. Suppose that 60% of those without strong party affiliation voted for Binton and 40% voted for Clush.

A) What is the probability that a randomly selected voter from this town favors R and voted for Clush?

B) Calculate the probability that a randomly selected voter from this town voted for Binton.

C) Calculate the probability that someone who voted for Binton is a D.

Explanation / Answer

a) probability that a randomly selected voter from this town favors R and voted for Clush =P(R)*P(Clush|R)

                                                   =0.65*0.72=0.468

b) probability that a randomly selected voter from this town voted for Binton =P(R)*P(binton|R)+P(D)*P(Binton|D)+P(None)*P(Binoton|None) =0.65*0.28+0.20*0.82+0.15*0.60=0.436

c) probability that someone who voted for Binton is a D =P(D)*P(Binton|D)/P(Binton) =0.20*0.82/0.436=0.3761

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