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 atleast four questions, is

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

Answer 1

Answer: (D)

$\frac{3}{64}$

Firstly, probability of getting exactly $4$ correct answers $=$ $3$ correct MCQ and a T/F $+$ $2$ correct MCQ and $2$ T/F

$\Rightarrow \frac{1}{4}.\frac{1}{4}.\frac{1}{4}.(\frac{2}{1}).\frac{1}{2}.\frac{1}{2}+(\frac{3}{2}).\frac{1}{4}.\frac{1}{4}.\frac{3}{4}.\frac{1}{2}.\frac{1}{2}=\frac{11}{256}$

Now, probability of getting exactly $5$ correct answers$=\frac{1}{4}.\frac{1}{4}.\frac{1}{4}.\frac{1}{2}.\frac{1}{2}=\frac{1}{256}$

So, total probability $=\frac{11}{256}+\frac{1}{256}=\frac{3}{64}$

So, option D cs correct.