In a multiple – choice question there are four alt

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 questions only if he ticks the correct answers. The candidate decides to tick the answers at random, if he is allowed up to three chances to answer the questions, find the probability that he will get marks in the questions.

Jitender Pal · Accepted Answer

Hello Student,

Please find the answer to your question

The total number of ways of ticking the answers in any one attempt = 2⁴ - 1 = 15.

The student is taking chance at ticking the correct answer, It is reasonable to assume that in order to derive maximum benefit, the three solutions which he submit must be all different.

∴ n = total no. of ways = ¹⁵C₃

m = the no. of ways in which the correct solution is excluded ¹⁴C₃

Hence the required probability = 1 - ¹⁴ C₃/¹⁵ C₃ = 1 – 4/5 = 1/5

ALTERNATE SOLUTION:

The candidate may tick one or more of the alternatives. As each alternative may or may not be chosen, the total numbers of exhaustive possibilities are 2⁴ - 1 = 15.

Therefore the prob. that the questions are correctly answered by candidate is 1/15.

As such the candidate may be correct on the first, second or third chance. As these events are mutually exclusive, the total probability will be given by

= 1/15 + 14/15 x 1/14 + 14/15 x 13/14 x 1/13 = 1/15 + 1/15 + 1/15 = 3/15 = 1/5

Thus the probability that the candidate gets marks in the question is 1/5.

Thanks
Jitender Pal
askIITians Faculty

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