In a multiple choice question there are four alternative answers of which one or more than one is correct. A candidate will get marks on 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, the probability that he will get marks on it is given by :

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${(14 / 15)}^{3}$

1/5

${(1 / 15)}^{3}$

$1 - {(14 / 15)}^{3}$

answer is C.

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Detailed Solution

total no of ways of answering is 15. Out of 15 combinations only one is correct. The probability of ticking the answer at the first .. is $\frac{1}{15},$ that of 2nd is $\frac{14}{15} . \frac{1}{14} = \frac{1}{15}$ and that of third is $\frac{14}{15} . \frac{13}{14} . \frac{1}{13} = \frac{1}{15} .$ $∴$ probability that the student will get marks for the question if he is allowed into 3 chances $= 3 (\frac{1}{15}) = \frac{1}{5} .$