Multiple choice

In a multiple choise question there are four alternative answers, of which one or more are correct. A candidate will get marks in the question only if be ticks all the correct answers.The candidate decides to tick answers at random. If he is allowed upto three chances to answer the question, find the probability that he will get marks in the question.

  1. $\displaystyle \dfrac{4}{5}$
  2. $\displaystyle \dfrac{1}{5}$
  3. $\displaystyle \dfrac{2}{5}$
  4. $\displaystyle \dfrac{3}{5}$
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B Correct answer
AI explanation

The candidate attempts up to three different random guesses from the 15 possible non-empty subsets of the four answers. Exactly one subset is the correct combination, so the probability of guessing correctly on any single attempt is 1/15. The probability of failing on the first attempt is 14/15, failing on the second is 13/14, and failing on the third is 12/13. The probability of getting marks is 1 minus the product of these failures: 1 minus (14/15 times 13/14 times 12/13), which simplifies to 1 minus 12/15, resulting in 3/15 or 1/5.

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