3
QuizMultiple Choice

Binomial Distribution — Quiz

Question 3 • Algebra II

According to a poll, 30 percent of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exactly 2 voters will be in favor of the ballot initiative? Round the answer to the nearest thousandth. cap p times k successes is equal to n cap c sub k p to the k th power open paren 1 minus p close paren raised to the n minus k power n cap c sub k is equal to the fraction with numerator n factorial and denominator open paren n minus k close paren factorial times k factorial

Answer
A
0 point 0 2 4
B
0 point 3 0 9
C
0 point 1 3 2
D
0 point 0 3 1

Explanation

Use the binomial probability formula with n = 5, k = 2, and p = 0.30. The probability is C(5, 2)(0.30)²(0.70)³ = 10 × 0.09 × 0.343 = 0.3087, which rounds to 0.309. The correct choice is 0.309.

AI-written and checked against the verified answer.

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