Multiple choice

In a multiple choice question there are five 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 answers. The candidate ticks the answers at random. If the probability of the candidate getting marks on the question is to be greater than or equal to 1/3, find the least number of chances he should be allowed

  1. $10$
  2. $11$
  3. $20$
  4. $22$
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B Correct answer
AI explanation

Since there are 5 options and one or more can be correct, the total number of possible answer combinations is 2 to the power of 5, minus 1, which is 31. If the candidate is allowed n attempts, the probability of getting marks is n divided by 31, so we need n to be greater than or equal to 31 divided by 3. Solving this gives n as at least 10.33, meaning the least integer number of chances is 11.

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