Question

A Mathematics paper consists of 12 questions of which not more than ten are to be answered. Given that the number of candidates who answer ten questions is equal to the number of candidates who answer nine questions only. Find the probability that a candidate chosen at random from among these two sets of candidates will have selected questions 1, 2 and 3 if all the questions have the same chance of being selected.​

Answer 1

The probability that a candidate chosen at random from among these two sets of candidates will have selected questions 1, 2 and 3 is 0.4179.

How to calculate probability?

The probability that a candidate chosen at random from among these two sets of candidates will have selected questions 1, 2 and 3 will ba calculated thus:

= [(9C6 /12C9) × 1/2] + [(9C7)/12C10) × 1/2]

= 42/220 + 18/66

= 0.1909 + 0.2727

= 0.4179

In conclusion, the probability is 0.4179.

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