Question:
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :
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Use the binomial distribution with \(n = 5\), \(p = \frac{1}{3}\) and add \(P(X=4) + P(X=5)\).
Updated On: Nov 13, 2026
- \(\frac{17}{3^5}\)
- \(\frac{13}{3^5}\)
- \(\frac{11}{3^5}\)
- \(\frac{10}{3^5}\)
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The Correct Option is C
Solution and Explanation
Each guess is correct with probability \(p = \frac{1}{3}\), wrong with \(q = \frac{2}{3}\); \(X \sim B(5, \frac{1}{3})\).
\(P(X=4) = {}^5C_4 \left(\frac{1}{3}\right)^4 \frac{2}{3} = \frac{5 \cdot 2}{3^5} = \frac{10}{3^5}\).
\(P(X=5) = \left(\frac{1}{3}\right)^5 = \frac{1}{3^5}\).
\(P(X \ge 4) = \frac{10 + 1}{3^5} = \frac{11}{3^5}\).
Answer: (3) \(\frac{11}{3^5}\)
\(P(X=4) = {}^5C_4 \left(\frac{1}{3}\right)^4 \frac{2}{3} = \frac{5 \cdot 2}{3^5} = \frac{10}{3^5}\).
\(P(X=5) = \left(\frac{1}{3}\right)^5 = \frac{1}{3^5}\).
\(P(X \ge 4) = \frac{10 + 1}{3^5} = \frac{11}{3^5}\).
Answer: (3) \(\frac{11}{3^5}\)
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