Question

A Bag contains 5 Red, 4 Green and 3 Black balls. Three balls are drawn out from it at random. Find the probability of drawing exactly 2 red balls.

Answer 1

On the 1st draw, probability of selecting 1 of the 5 red balls from a total of 12 balls = $\frac{5}{12}$
On the 2nd draw, probability of selecting 1 of the 4 remaining red balls from a total of 11 remaining balls = $\frac{4}{11}$
On the 3rd draw, probability of selecting 1 of the 7 non-red balls from a total of 10 remaining balls = $\frac{7}{10}$

Therefore, the probability of drawing exactly 2 red balls = $\frac{5}{12}\times \frac{4}{11}\times \frac{7}{10}=\frac{7}{66}$