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?

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

 [tex] \dfrac{1}{2} \cdot \dfrac{3}{10} \cdot \dfrac{1}{5} = \dfrac{3}{100} [/tex].

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