Three six-sided dice are rolled. The six sides of each die are numbered 1–6. Let A be the event that the first die shows an even number, let B be the event that the second die shows an even number, and let C be the event that the third die shows an even number. Also, for each i = 1, . . . , 6, let Ai be the event that the first die shows the number i, let Bi be the event that the second die shows the number i, and let Ci be the event that the third die shows the number i. Express each of the following eventsin terms of the named events described above:
a. The event that all three dice show even numbers
b. The event that no die shows an even number
c. The event that at least one die shows an odd number
d. The event that at most two dice show odd numbers
e. The event that the sum of the three dices is no greater than 5