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 - $P_w= \dfrac{5}{10} = \dfrac{1}{2}$;
2. the probability to choose red ball - $P_r= \dfrac{3}{10}$;
3. the probability to choose black ball - $P_b= \dfrac{2}{10}= \dfrac{1}{5}$.
Using the product rule you can conclude that the probability that all 3 balls are different colors is:

 $\dfrac{1}{2} \cdot \dfrac{3}{10} \cdot \dfrac{1}{5} = \dfrac{3}{100}$.