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Q.

In a multiple-choice question, there are five alternative answers, of which one or more than one are correct. A candidate will get marks on the question if he ticks all the correct answers. So he decides to tick answers at random, if the least number of chances, he should be allowed so that the probability of his getting marks on the question exceeds 1/8 is K, then K=
(The student always attempt the question)

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answer is 4.

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Detailed Solution

The probability that he get marks $= \frac{1}{31}$
The probability that he get marks in second trial is $\frac{30}{31} \times \frac{1}{30} = \frac{1}{31}$
The probability that he get marks in third trial is $\frac{1}{31}$
Continuing this process the probability from r trial is $\frac{r}{31} > \frac{1}{8}$
$\Rightarrow r > \frac{31}{8} \Rightarrow r = 4$

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