Consider the events A and B given in problem 3 on the first homework set.
(a) Recall the experiment in 3(a): throwing 3 fair dice and the following events.
A = “At least one of the dice shows a 6”, B = “The dice show the same number”.
Compute P (A), P (B), P (B|A) and P (A|B) for problem 3(a).
(b) Consider the same setting as 3(c), where a bag contains 3 red balls and 1 blue ball.
We randomly draw two balls, one at a time, where after a ball is drawn, it gets put
back into the bag before the next draw. Recall the events A = “At least one of the
balls drawn is blue”, B = “Both balls have the same color”. Compute P (A), P (B),
P (B|A) and P (A|B)