Find the probability that there are 2 red and 1 blue disc

Question

A bag contains 5 red discs and 4 blue discs. If 3 discs are drawn from the bag without replacement then find the probability that there are 2 red abd 1 blue discs.

Answer 1

If R=red disc and B=blue disc, the possible outcomes are RRB, RBR, BRR. The probability of each can be calculated:

RRB: (5/9)(4/8)(4/7)=10/63

RBR: (5/9)(4/8)(4/7)=10/63

BRR: (4/9)(5/8)(4/7)=10/63

So the probability for each outcome is the same and the total probability is the sum of these: 10/21.