The table describes the voters in a certain district. Assume a voter is chosen a

Question

The table describes the voters in a certain district. Assume a voter is chosen at random. Find the following probabilities. Republican Democrat Independent 40 63 Male Female 2 a. The probability that the voter is a Republican is (Type an integer or decimal rounded to three decimal places as needed.) b. The probability that the voter is male is (Type an integer or decimal rounded to three decimal places as needed.) c. The probability that the voter is male, given that they are a Republican is (Type an integer or decimal rounded to three decimal places as needed.) d. The probability that the voter is a Republican given that they are male is (Type an integer or decimal rounded to three decimal places as needed.)

Explanation / Answer

Following table shows the row and column total:

()

Out of 123 voters, 72 are republican so

P(republican) = 72 /123 = 0.585

(b)

Out of 123 voters, 105 are male so

P(male) = 105 /123 = 0.854

(c)

Out of 105 males, 63 are republican so

P(republican|male) = 63/105 = 0.600

(d)

Out of 72 republicans, 63 are male so

P(male | republican) = 63/72 = 0.875

Republican Democrat Independent Total Male 63 40 2 105 Female 9 7 2 18 Total 72 47 4 123

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