A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a stu - Mathematics MCQ JEE Main 2026 | ExamTest.live

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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:

Solution & Step-by-step Explanation

This follows a Binomial distribution B (n, p) where: n = 5 p = \frac{1}{3} (probability of guessing correct) q = \frac{2}{3} (probability of guessing wrong)We need P (X \geq 4) = P (X = 4) + P (X = 5) . P (X = 4) = (4 5) (\frac{1}{3})^{4} (\frac{2}{3})^{1} = 5 \cdot \frac{2}{3 ^{5}} = \frac{10}{3 ^{5}} P (X = 5) = (5 5) (\frac{1}{3})^{5} (\frac{2}{3})^{0} = 1 \cdot \frac{1}{3 ^{5}} = \frac{1}{3 ^{5}} P (X \geq 4) = \frac{10}{3 ^{5}} + \frac{1}{3 ^{5}} = \frac{11}{3 ^{5}}

Try it yourself before checking the explanation above.

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:

\frac{13}{3^5}

\frac{11}{3^5}

\frac{10}{3^5}

\frac{17}{3^5}

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