One urn contains three red balls, two white balls, and one blue ball. A second urn contains one red ball, two white balls, and three blue balls.
a) One ball is selected at random from each urn:
i) Describe sample space for this experiment.
ii) Find the probability that both balls will be of the same color.
b) The balls in the two urns are mixed together in a single urn, and then a sample of three is drawn. Find the probability that the three colors are represented, when
i) sampling with replacement
ii) without replacement.
I will give hints and leave the rest to you:
a) i) The sample space is the set of possibilities. What are all possible outcomes of this experiment?
ii) To calculate probability of both balls being red, we calculate each probability separately and multiply them as they are independent. Probability of first ball being red is $\frac{3}{6}$ and second ball being red is $\frac{1}{6}$. Hence, $\frac{3}{36}$. The rest are easy to compute.
b) When sampling with replacement, the probability is $\frac{4}{12} * \frac{4}{12} * \frac{4}{12} * 3!$. Without replacement, it's $\frac{4}{12} * \frac{4}{11} * \frac{4}{10} * 3!$