Construct the probability distribution for X (without using binomial distributio

Question

Construct the probability distribution for X (without using binomial distribution since we haven't learned that yet)

5.35 Public Policy and Political Science According to a January 2013 survey by the Pew Research Center, the percent- age of Americans who trust the government in Washington has decreased steadily since Bill Clinton left office. Today, approximately 30% of"Americans say they trust the govern- ment (always or most of the time). Suppose three Americans are selected at random. Let X be the number who trust the government.

Explanation / Answer

When 3 people selected, the value of x can be 0,1,2 or 3

P(an american truisting government0 = 0.3

P(an american not trusting government) = 1 - 0.3 = 0.7

P(X = 0) = All three does not trust government = 0.7 x 0.7 x 0.7 = 0.343

P(X = 1) = 0.7x0.7x0.3 + 0.7x0.3x0.7 + 0.3x0.7x0.7 = 0.441

P(X = 2) = 0.3x0.3x0.7 + 0.3x0.7x0.3 + 0.7x0.3x0.3 = 0.189

P(X = 3) = 0.3x0.3x0.3 = 0.027

Probability distribution of x is given below

X 0 1 2 3 P(X) 0.343 0.441 0.189 0.027

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