# Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.

Let S be the sample space of throwing two dice and the two numbers are different, then the sample space is

S = {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5)}

n(S) = 30

Let B be the event that the sum if the numbers on the dice is 4, then the sample space becomes

B = {(1, 3), (3, 1)}, n(B) = 2

So the probability of the event ‘the sum of numbers on the dice is 4’ is

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