Suppose 85 of republicans voted for John McCain in the 2008

Suppose 85% of republicans voted for John McCain in the 2008 presidential election. Furthermore, suppose 75% of non-Republicans (Democrats and Independents)voted for Obama(not McCain). Finally, suppose 45% of the voter were Republicans. 1.What is the probability that any voter voted for McCain?

2. What is the probability of a voter both being a Republican and voting for Obama?

3.If a voter voted for McCain, what is the probability that he/she is not a Republican?

Solution

1)

P(Mc) = P(Re) P(Mc|Re) + P(nonRe) P(Mc|NonRe)

= (0.45)(0.85) + (1-0.45)(1-0.75)

= 0.52 [answer]

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2)

P(Re and Ob) = P(Re) P(Ob|Re) = 0.45(1-0.85) = 0.0675 [answer]

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3)

P(non Re|Mc) = P(non Re and Mc) / P(Mc)

= [P(non Re) P(Mc|Non Re)] / P(Mc)

= [(1-0.45)(1-0.75)] / 0.52

= 0.264423077 [answer]