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An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: Which pairs of these events are mutually exclusive?

3.     An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

             Which pairs of these events are mutually exclusive?

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For two elements to be mutually exclusive, there should not be any common element amongst them.

Also, A = {(3,6), (4,5), (5, 4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6)}

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

C = {(3,6), (6,3), (5, 4), (4,5), (6,6)

Now,  A \cap B = \phi      (no common element in A and B)

Hence, A and B are mutually exclusive

Again, B \cap C = \phi     (no common element in B and C)

Hence, B and C are mutually exclusive

Again, C \cap A = {(3,6), (6,3), (5, 4), (4,5), (6,6)}

Therefore, 

A and B, B and C are mutually exclusive.

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