7
QuizMultiple Choice

Binomial Distribution — Quiz

Question 7 • Algebra II

Johnni guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that she got exactly 3 questions 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 4 2 2
B
0 point 2 0 8
C
0 point 7 9 2
D
0 point 0 0 4

Explanation

Each guess has a 1/4 chance of being correct, so use the binomial probability for exactly 3 correct out of 8: C(8,3)(0.25)^3(0.75)^5. Since C(8,3) = 56, the probability is 56(0.25)^3(0.75)^5 ≈ 0.2076, which rounds to 0.208. The correct choice is 0.208.

AI-written and checked against the verified answer.

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