[Math] Probability in urns

Question

There are 3 urns labeled X, Y, and Z.

• Urn X contains 4 red balls and 3 black balls.
• Urn Y contains 5 red balls and 4 black balls.
• Urn Z contains 4 red balls and 4 black balls.

One ball is drawn from each of the 3 urns. What is the probability that, of the 3 balls drawn, 2 are red and1 is black?

I could not understand this problem properly and find out how solution is obtained.

Answer 1

Add up the probabilities of all mutually exclusive cases

• RRB $\ \longrightarrow \ \dfrac{4}{7}\cdot \dfrac{5}{9}\cdot \dfrac{4}{8}$
• RBR etc
• BRR etc