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# Probability (when identical)

There are 6 identical red balls, 6 identical white balls and 6 identical black balls distributed randomly into two different boxes $$B_1$$ and $$B_2$$. Find the probability that:

1. Both boxes have the same number of balls.
2. Both boxes have at least one ball of each color.

Provide a full solution (without any use of intuition).

Note by Karthik Venkata
1 week ago

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Instead of asking for a full solution, why don't you show us where you're stuck on and what you've tried?

- 6 days, 16 hours ago

If we write down the sample space, all outcomes are not equally likely. I am not sure what to do in such cases.

- 6 days, 7 hours ago

Hint:

Q1: 9 balls goes B1, 9 balls goes B2. Binomial distribution

Q2: Find the complementary probability.

- 6 days, 3 hours ago