Two dice are thrown and the sum of the numbers 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 a multiple of 3’
.C: ‘the sum is less than 4’
.D: ‘the sum is greater than 11’.
Which pairs of these events are mutually exclusive?

Explanation

sample space = S = {(x,y) : x,y =1, 2, 3, 4, 5, 6}

i.e., 5 = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (2,1),………… (2,6), (3,1), ……….. ,(3,6), (4,6),……….. (5,1), …………… (5,6), (6,1),(6,2),(6,3),(6,4), (6,5),(6,6)}


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


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


C = {(1,1),(1,2),(2,1)} D = {(6,6)}

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