Question

A box contains 35 gems, of which 10 are real diamonds and 25 are fake diamonds. Gems are randomly taken out of the box, one at a time without replacement. What is the probability that exactly 2 fakes are selected before the second real diamond is selected

Answer 1

Explanation:

The total number of ways of selecting 3 gems of any kind without replacement is 35 * 34 * 33 = 39270

Now selecting 2 gems from 25 is 25C2

25 C 2 = 25 * 24/2 = 300

Selecting one good gem is 10

Total selection = 300 * 10 = 3000

P(gems) = 3000 / 39270

P(gems) = 300/3927

P(gems) = 100/1309