In a multiple-choice question there are four alternative answer, of which one of more are correct. A candidate will get marks only if he ticks all the answers. The candidate decides to tick at random. He is allowed upto three chance to answer the question. Find the probability that he will get marks for the question.

Explanation

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`