Question

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

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

Answer 1

The correct option is B $\frac{1}{5}$

The total number of ways to answer the question ${}^4{C}_1{+}^4{C}_2{+}^4{C}_3{+}^4{C}_4=2^4-1=15$
Then $P$(getting marks) = $P$(correct answer in I chance) +$P$(correct answer in II chance) +$P$(correct answer in III chance)
$=\frac{1}{5}+(\frac{14}{15}.\frac{1}{14})+(\frac{14}{15}.\frac{13}{14}.\frac{1}{13})=\frac{3}{15}=\frac{1}{5}$