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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
3 months 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?

Pi Han Goh - 3 months ago

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

Karthik Venkata - 3 months ago

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Hint:

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

Q2: Find the complementary probability.

Pi Han Goh - 3 months ago

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@Chew-Seong Cheong Sir, please help if you can :)

Karthik Venkata - 3 months ago

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