Answer to Question #145631 in Statistics and Probability for Randal Rodriguez

Question #145631
1. A box containing 6 black balls, 4 green balls, and 3 red balls. 3 balls are drawn in succession, wherein each ball being replaced in the box before the next draw is made. What is the probability that

(a) all 3 are the same color?
(b) each color is represented?
1
Expert's answer
2020-11-23T11:09:51-0500

a). The probability that 3 black balls are drown is: "p_1=(\\frac{6}{13})^3".

The probabiltiy that green balls are drawn is: "p_2=(\\frac{4}{13})^3" .

For red balls we have: "p_3=(\\frac{3}{13})^3" . We used the multiplication rule to get these probabilities (see https://stattrek.com/probability/probability-rules.aspx) The probability that all three balls have the same color is: "p=p_1+p_2+p_3=\\frac{27+216+64}{2197}\\approx0.1397."

b). The probability that all balls have different colors is: "3!\\frac{3\\cdot4\\cdot6}{13^3}\\approx0.1966" .We used the factor 3!, since drawn balls can be situated in different order.


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