Part c asks us to find the probablity that the selected die has three red faces given that the first three rolls came up Red.
Let D3 denote it being Dice3, and Ri denote that the ith roll is red and what we're trying to find becomes the following:
P(D3|R1R2R3)
Following Bayes rule we can get:
P(D3R1R2R3)\P(R1R2R3)
Since we know that the probability of D3 intersect R1R2R3 is the same thing as the probability that we picked D3 and we rolled 3 red faces - we should be able to rewrite as:
[P(R1R2R3|D3)P(D3)]/P(R1R2R3)
where R1R2R3 can be found in a similar process to finding it in problem 2.
Hope that helps!
