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.

Answer

`1/5`

Explanation

Since the questions is multiple choice in which one or more than one options are correct, correct options may be one, two three or four.
`therefore` Total number of ways of ticking one or more alternatives out four `=""^(4)C_(1)+""^(4)C_(2)+""^(4)C_(3)+""^(4)C_(4)=15`
Out of these 15 combinations, only one combination is correct.
`therefore` Probability of thcking the alternative correctly at the first trial,
`P(T_(1))=1/15`
Probability of ticking the answer correctly in second trial,
`P(T_(1)'nnT_(2))=P(T_(1)')P(T_(2)//T_(1)')`
`=14/15xx1/14xx1/13=1/15`
Thus, the probability that the candidate will get marks on the question if he is allowed up to three trials
`=1/15xx13/15+1/15=1/5`