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. Acandidate 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. $\frac{3}{100}$

Answer 1

Answer: (D)

$\frac{3}{100}$

Given an objective type test paper contains $5$ questions out of $5$ questions, $3$ questions have five options each.

Let there $3$ questions be denoted as A,B, and C. The other two questions contain $2$ parts each. Let they be denoted as D and E.

Let the probability of choosing the correct answer in the first three questions be $1/5$

$\therefore$ Probability of choosing wrong answer $=4/5$

The probability of choosing correct answer in questions $4$ and $5$ $=1/2$ and probability of choosing wrong answer $=1/2$

$P$ (at least $4$ questions are correct )

$=\frac{1}{5}.\frac{1}{5}.\frac{1}{5}.\frac{1}{2}.\frac{1}{2}+\frac{1}{5}.\frac{1}{5}.\frac{1}{5}.\frac{1}{2}.\frac{1}{2}+\frac{1}{5}.\frac{1}{5}.\frac{4}{5}.\frac{1}{2}.\frac{1}{2}+\frac{1}{5}.\frac{4}{5}.\frac{1}{5}.\frac{1}{2}.\frac{1}{2}+\frac{4}{5}.\frac{1}{5}.\frac{1}{5}.\frac{1}{2}.\frac{1}{2}$

$=\frac{1+1+4+4+4}{500}$

$=\frac{14}{500}$

$\Rightarrow P$ (all questions are correct ) $=\frac{1}{5}.\frac{1}{5}.\frac{1}{5}.\frac{1}{2}.\frac{1}{2}=\frac{1}{500}.$

$=\frac{14+1}{500}$

$=\frac{3}{100}.$