Forty-six percent of a survey of 900 voters favor the democratic candidate. Of t

Question

Forty-six percent of a survey of 900 voters favor the democratic candidate. Of the 400 voters age 30 or less, 36% favored the democratic candidate. What is the probability that a. If a voter favors the democratic candidate they are over 30 years old? b. If a voter is over 30 years old they favor the democratic candidate? Forty-six percent of a survey of 900 voters favor the democratic candidate. Of the 400 voters age 30 or less, 36% favored the democratic candidate. What is the probability that a. If a voter favors the democratic candidate they are over 30 years old? b. If a voter is over 30 years old they favor the democratic candidate? a. If a voter favors the democratic candidate they are over 30 years old? b. If a voter is over 30 years old they favor the democratic candidate?

Explanation / Answer

Probability that a voter is democratic P(D) = 0.46

Probability that the age of voter is 30 or less P(B) = 400/900 = 0.4444 and P(B') = 0.5556

P(D and B) = 0.16 (=0.36*400/900)

P(D and B') = 0.3 (total 0.46*900=414 supports democratic out of this 0.36*400=144 voters age 30 or less, this means 414-144=270 democratic supports are over 30 years old. Hence probability 270/900=0.3)

(A)

P(B'|D) = P(D and B') / P(D) = 0.3/0.46 = 0.6522

(B)

P(D|B') = P(D and B')/P(B') = 0.3/0.5556 = 0.54

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