Question

In a multiple choice question, there are four alternative answer of which one or more than one is correct. A candidate will get marks on the question only if he ticks all the correct answer. The candidate decides to tick all the correct answer. The candidate decides to tick answers at random. If he is allowed up to three chances to answer the question, the probability that he will get marks on it is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

Answer: (D)

$\frac{1}{5}$

The total number of ways of ticking one or more alternatives out of $4$ is ${}^4{C}_1{+}^4{C}_2{+}^4{C}_3{+}^4{C}_4=15$
Out of these $15$ combination, only one is correct.
The probability of ticking the alternatives correct at the first trail $\frac{1}{15}$,
that at the second trail is $\frac{14}{15}.\frac{1}{14}=\frac{1}{15}$
and that at the third trail is $\frac{14}{15}.\frac{13}{14}.\frac{1}{13}=\frac{1}{15}$
Then, the probability that the candidate will get marks on the question is he is allowed three trails is
$\frac{1}{15}+\frac{1}{15}+\frac{1}{15}=\frac{3}{15}=\frac{1}{5}$