We flip coin. If the coin is HEADS, then we roll three die and record their total. If the coin is TAILS, then we roll two dice and record sum. Find the following
(1) Given that coin flip is TAILS, find the probability of a sum of 11.
(2) Compute the probability of getting a sum equal to 11.
(3) Given that the sum is 11, what is the probability that the flip was TAILS?
(4) Given that the flip is HEADS and that the sum is at least 11, what is the probability of a sum of 15?
(5) Determine the probability of a sum of 3?