Question

An objective type test paper has $5$ questions. Out of these $5$ questions, $3$ questions have four options each $(A, B, C, D)$ with one option being the correct answer. The other $2$ questions have two options each, namely True and False. A candidate randomly ticks the options. Then the probability that he/she will tick the correct option in at least four questions, is

• A. $\frac{5}{32}$
• B. $\frac{3}{128}$
• C. $\frac{3}{256}$
• D. $\frac{3}{64}$

Answer 1

Answer: (D)

$\frac{3}{64}$

Answer 2

Total sample space, $n(S)=4^{3} \cdot 2^{2}$ and total number of favourable cases
$n(E) =\left({ }^{3} C_{1} \cdot 3+{ }^{2} C_{1} \cdot 1\right)+1$
Required probability $= \frac{n(E)}{n(S)}$
$= \frac{{ }^{3} C_{4} \cdot 3+{ }^{2} C_{1} \cdot 1+1}{4^{3} \cdot 2^{2}}=\frac{3 \cdot 3+2+1}{4^{3} \cdot 4}$
$=\frac{12}{64 \cdot 4}=\frac{3}{64}$