6
QuizMultiple Choice

Binomial Distribution — Quiz

Question 6 • Algebra II

Van guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got exactly 1 question correct? 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 3 3
B
0 point 4 6 1
C
0 point 7 3 3
D
0 point 2 6 7

Explanation

Use the binomial probability formula with n = 8, k = 1, and p = 1/4, since each guess has a 1-in-4 chance of being correct. The probability is 8C1(0.25)^1(0.75)^7 ≈ 0.26697, which rounds to 0.267. The correct choice is D, 0.267.

AI-written and checked against the verified answer.

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