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A multiple-choice exam has 10 questions each with 5 options. The probability that a student getting **8 or more correct** by random guessing is approximately:
A~$10^{-3}$
B~$10^{-5}$
C~$0.5$
D~$0.5 \cdot (1/5)^8$
Answer & Solution
Correct answer: B. ~$10^{-5}$
$p = 1/5 = 0.2$. $P(X \geq 8) = P(8) + P(9) + P(10)$ ≈ ${}^{10}C_8 (0.2)^8 (0.8)^2 + {}^{10}C_9 (0.2)^9 (0.8) + (0.2)^{10}$ ≈ $7.4\times10^{-5} + 4\times10^{-6} + 10^{-7}$ ≈ $\boxed{8 \times 10^{-5}}$. Moral: don't bet on guessing your way through an exam!
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