Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?

One Answer on this Question

1. Out of 10 persons, 4 are graduates; so, (10 – 4) = 6 are under-graduates.

   If there is no restriction, any three can be chosen from the ten in (10C3) = 120 ways.

   Now, if all three chosen are under-graduates; it can take place in (6C3) = 20 ways.

   Therefore, the probability that there will be no graduate among the three chosen = (20 / 120) = (1 / 6).

   Therefore, the probability that there will be at least one graduate among the three chosen = {1 – (1 / 6)} = (5 / 6) = 0.8333.

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