Answer:
E'∪F'=[1, 1], [1, 3], [1, 5], [3, 1], [3, 3] [3, 5],[5, 1], [5, 3], [5, 5], [2, 2], [2, 4], [2, 6]
[4, 2],[4, 4], [4, 6], [6, 2], [6, 4], [6, 6]
Step-by-step explanation:
Sample Space of the Two Dice is:
[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6]
[2, 1], [2, 2], [2, 3], [2, 4], [2, 5], [2, 6]
[3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6]
[4, 1], [4, 2], [4, 3], [4, 4], [4, 5], [4, 6]
[5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6]
[6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [6, 6]
E=At least one die shows an even number.
Sample Space of E
[1, 2], [1, 4], [1, 6]
[2, 1], [2, 2], [2, 3], [2, 4], [2, 5], [2, 6]
[3, 2] [3, 4], [3, 6]
[4, 1], [4, 2], [4, 3], [4, 4], [4, 5], [4, 6]
[5, 2], [5, 4], [5, 6]
[6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [6, 6]
Complement of E
[1, 1], [1, 3], [1, 5], [3, 1], [3, 3] [3, 5],[5, 1], [5, 3], [5, 5]
F=At least one die shows an odd number
Sample Space of F
[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6]
[2, 1], [2, 3], [2, 5],
[3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [3, 6]
[4, 1], [4, 3], [4, 5]
[5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6]
[6, 1], [6, 3], [6, 5],
Complement of F
[2, 2], [2, 4], [2, 6]
[4, 2],[4, 4], [4, 6]
[6, 2], [6, 4], [6, 6]
Therefore:
E'∪F'=[1, 1], [1, 3], [1, 5], [3, 1], [3, 3] [3, 5],[5, 1], [5, 3], [5, 5], [2, 2], [2, 4], [2, 6]
[4, 2],[4, 4], [4, 6], [6, 2], [6, 4], [6, 6]
