Q28 / 50 · Manipal (MET) 2022 · Mathematics
A multiple choice examination has 5 questions. Each question has 4 alternative answer of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing is
- A$\frac{1}{4^5}$
- B$\left(\frac{3}{4}\right)^4$
- Correct answerC$\frac{1}{4^3}$
- D$\frac{3}{4^5}$
Solution
Probability of guessing a correct answer, $p=\frac{1}{4}$ and probability of guessing a wrong answer $q=\frac{3}{4}$
So, the probability of guessing 4 or more correct answer
$\begin{aligned} P(X \geq 4) & ={ }^5 C_4\left(\frac{1}{4}\right)^4 \cdot\left(\frac{3}{4}\right)+{ }^5 C_5\left(\frac{1}{4}\right)^5 \\ & =5 \cdot \frac{1}{4^4} \cdot \frac{3}{4}+\frac{1}{4^5} \\ & =\frac{15}{4^5}+\frac{1}{4^5}=\frac{16}{4^5}=\frac{4^2}{4^5}=\frac{1}{4^3}\end{aligned}$
Hence, the correct answer is option: 'C'.