One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. Write the sample space showing all possible outcomes. What is the probability that two black balls are chosen? What is the probability that two balls of opposite colour are chosen?

Explanation

To solve the problem step by step, we will first identify the sample space, then calculate the probabilities for the two scenarios: choosing two black balls and choosing two balls of opposite colors.

### Step 1: Identify the Sample Space

1. **Choosing an Urn**: There are two urns:
- Urn 1 contains: B1, B2, W (2 black balls and 1 white ball)
- Urn 2 contains: B, W1, W2 (1 black ball and 2 white balls)

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