A box contains 4 red balls, 5 blue balls, and 6 green balls. Five balls are removed from the box, at random. (In your solutions to the following questions, please use appropriate notations and/or words to justify all values that are given as part of your solutions.)

 

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[5] (a) What is the probability that at most one of the removed balls is red? (b) What is the probability that the removed balls contain at least one ball of each of the three colours? [5] (c) Find the expectation and variance for the number of green balls among those removed. [10] [5] (a) What is the probability that at most one of the removed balls is red? (b) What is the probability that the removed balls contain at least one ball of each of the three colours? [5] (c) Find the expectation and variance for the number of green balls among those removed. [10]

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