Two dice are thrown at the same time. Find the probability of getting (i) Same number on both dice. (ii) different number of both dice.

Solution:

Total number of possible outcomes, n(s) = 36

(i) Let E1 be the event of getting same number on both dice. 

Possible outcomes = (1, 1), (2, 2), (3,3), (4, 4), (5, 5) and (6, 6)

Number of possible outcomes, n(E1) = 6

Required probability, P(E1) = n(E1)/n(s) = 6/36 = ⅙

(ii) Let E2 be the event of getting different number on both dice. 

So, number of possible outcomes = 36 – number of possible outcomes for same number on both dice

= 36 – 6 = 30 

Required probability, P(E2) = 30/36 

= 5/6

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