Probability Ques 137
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 (2013 Main)
(a) $\frac{17}{3^{5}}$
(b) $\frac{13}{3^{5}}$
(c) $\frac{11}{3^{5}}$
(d) $\frac{10}{3^{5}}$
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Answer:
Correct Answer: 137.(c)
Solution:
Formula:
- Probability of guessing a correct answer, $p=\frac{1}{3}$ and probability of guessing a wrong answer, $q=2 / 3$
$\therefore \quad$ The probability of guessing a 4 or more correct answers $={ }^{5} C _4 (\frac{1}{3}) \cdot \frac{2}{3}+{ }^{5} C _5 (\frac{1}{3}){ }^{5}=5 \cdot \frac{2}{3^{5}}+\frac{1}{3^{5}}=\frac{11}{3^{5}}$
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