Disclaimer: This is for homework help.
I have those 2 above questions that I'm trying to solve. I'm trying to use Bayes' rule but completely confused as to how to apply to it. I'm also struggling to understand the difference between what part a and b are asking. It seems as if they are both asking for the same thing since the only possibility of having the remaining 2 balls having the same colour under the situation where a red ball has already been picked is that both balls are blue.
Start, rather than going straight into Bayes' Theorem, by drawing the tree diagram. What are the events?
The two parts are not asking the same thing, for when taking a red ball from the first box you are left with 1 blue ball, while taking a red ball from the second box leaves you with 2 blue balls. If we were to take one blue ball from each box., that leaves 0 in the first box, 1 in the second box. But the chances of picking each box were equally likely: 1/2. I will leave you to write down the final calculation.