Question

An urn contains 10 bails: 5 are white, 3 are red, and 2 are black. three balls are drawn at random, with replacement, from the urn. what is the probability that all 3 balls are different colors?

Answer 1

If three balls are drawn from 10 balls with replacment, then you should count:
1. the probability to choose white ball -
`P_w= (5)/(10) = (1)/(2)`;
2. the probability to choose red ball -
`P_r= (3)/(10)`;
3. the probability to choose black ball -
`P_b= (2)/(10)= (1)/(5)`.
Using the product rule you can conclude that the probability that all 3 balls are different colors is:


`(1)/(2) \cdot (3)/(10) \cdot (1)/(5) = (3)/(100)`.