Question

Suppose Aaron, a pollster in the very small county of Crankshaft, wants to gauge the popularity of a new tax plan proposed by the mayor. Crankshaft has only 40 registered voters. Of these voters, 22 are registered as Republicans, and 18 are registered as Democrats. Suppose Aaron conducts a random sample of 5 registered voters and asks them if they support the new tax plan. Let ? represent the number of Democrats in the population, and let ? represent the desired number of Democrats in Aaron's sample. Let ? represent the total population size, and let ? represent the size of Aaron's sample. Suppose Aaron wants to determine the probability that his random sample contains exactly 2 Democrats. Follow the steps to compute P(X=2), where X is the random variable representing the number of Democrats in Aaron's sample. First, compute the quantities (??) , (?−??−?) , and (??) without rounding. Each of these answers are whole numbers. Finally, use these values to calculate the probability that Aaron selects exactly 2 Democrats in his sample. Please round your answer to the nearest three decimal places.

Answer 1