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In a multiple choice question, there are...

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 the correct answer. The candidate decides to tick answers at a random. If he is allowed up to three chances to answer the question, then find the probability that he will get marks on it.

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As one more of the alternatives may be correct, the number of ways in which the question can be answered
`=""^4C_1+""^4C_2+""^4C_3+""^4C_4`
`=""^4C_0+""^4C_1+""^4C_2+""^4C_3+""^4C_4-1`
`=2^4-1=15`
As candidate is allowed three chance, he can mark his response in `""^(15)C_3` ways.
The no. of ways in which the candidate doesn't get marks
= The no. of ways in which he chooses 3 responses out of 14 wrong ones.
`therefore` Probability that the candidate doesn't answer `=(""^(14)C_3)/(""^(15)C_3)`
`=(14xx13xx12)/(15xx14xx13)=4/5`
Hence the probability of the complementary event, that is the candidate gets marks for the question
`=1-4/5=1/5`
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