Question:
A multiple choice examination has 5 questions. Each question has 4 alternatives of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing is
A multiple choice examination has 5 questions. Each question has 4 alternatives of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing is
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“4 or more” = 4 + 5 cases (don’t miss last term!).
Updated On: Apr 22, 2026
- \( \frac{1}{4^5} \)
- \( \left(\frac{3}{4}\right)^4 \)
- \( \frac{1}{4^3} \)
- \( \frac{3}{4^5} \)
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The Correct Option is D
Solution and Explanation
Concept:
Binomial probability:
\[
P = \sum P(X=4) + P(X=5)
\]
Step 1: Compute.
\[ P(4) = \binom{5}{4}\left(\frac{1}{4}\right)^4\left(\frac{3}{4}\right) \] \[ P(5) = \left(\frac{1}{4}\right)^5 \]
Step 2: Add.
\[ = \frac{15}{4^5} + \frac{1}{4^5} = \frac{16}{4^5} = \frac{3}{4^5} \]
Step 1: Compute.
\[ P(4) = \binom{5}{4}\left(\frac{1}{4}\right)^4\left(\frac{3}{4}\right) \] \[ P(5) = \left(\frac{1}{4}\right)^5 \]
Step 2: Add.
\[ = \frac{15}{4^5} + \frac{1}{4^5} = \frac{16}{4^5} = \frac{3}{4^5} \]
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