Two dice are thrown and sum of the number which come up on the dice is

1.	Two dice are thrown and sum of the number which come up on the dice is noted. Let us consider the following events associated with this experiment.A: the sum is even. B: the sum is less than 4. C: the sum is greater than 11. Which pair of these events are mutually exclusive?
Answer» When dice are thrown, sample space is– S = {(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)} A = {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6, (3, 1), (3, 5), 4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6), (3, 3)} B = {(1, 1), (1, 2), (2, 1)} C = {(5, 6), (6, 6)} Since, A ∩ B ≠ ϕ, B ∩ C ≠ ϕ, A ∩ C ≠ ϕ.

Two dice are thrown and sum of the number which come up on the dice is noted. Let us consider the following events associated with this experiment.A: the sum is even. B: the sum is less than 4. C: the sum is greater than 11. Which pair of these events are mutually exclusive?

Answer»

When dice are thrown, sample space is–

S = {(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)}

A = {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6, (3, 1), (3, 5), 4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6), (3, 3)}

B = {(1, 1), (1, 2), (2, 1)}

C = {(5, 6), (6, 6)}

Since, A ∩ B ≠ ϕ, B ∩ C ≠ ϕ, A ∩ C ≠ ϕ.

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