Use the additive law of probability if possible to solve the following problem

Question

A monkey is to demonstrate that she recognizes colors by tossing one red, one black, one white ball, one orange ball, and one purple ball into boxes of the same respective colors, one ball to a box. If the monkey has not learned the colors and merely tosses one ball into each box at random, find the probabilities of the following results: a. There are no color matches. b. There is exactly one color match.

Answer 1

Answer 2

1. 44/120 = 11/30.

2. 45 / 120 = 3 / 8

For #2, use the 0 correct boxes answer for 4 balls (9), and multiply by 5. Use the same denominator as in #1, 5!

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