Question

Ina multiple choice question, these are five alternative answers, of which one or more than one correct. A candidate will get marks on the question if he ticks all the correct answers. The candidate decides to tick answers at random. How many chances should he be allowed so that the probability of his getting marks on the question?

• A. $\frac{1}{4}$
• B. $\frac{1}{5}$
• C. $\frac{1}{2}$
• D. $\frac{1}{8}$

Answer 1

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

Total number of ways of ticking the answers in any attempt $2^4-1=15$
It is reasonable to assume that in order to derive maximum benefits,
the three solutions which he will submit must all be different.
$\therefore n=$ total number of ways $={}^{15}{C}_3$
$m=$ the number of ways in which the correct solution is excluded $={}^{14}{C}_3$
Hence, the required probability $=\frac{{}^{14}{C}_3}{{}^{15}{C}_3}=1-\frac{4}{5}=\frac{1}{5}$