Be very clear and explain each step in your proofs.
1) Experiment: Roll three 6-sided dice and flip a coin then record the results
a) Describe a suitable sample space for the experiment that contains equally likely outcomes.
b) Find the probability that the total sum of the three dice is 6 and the coin comes upHeads.
c) Find the probability that the total sum of the three dice is 6 or the coin comes upHeads.
d) Find the probability that exactly 2 of the dice rolled are 5's.e) Find the probability that at least 2 of the dice rolled are 5's