Q) Two dice are thrown at the same time. Determine the probability that:
(i)   the sum of the numbers on the two dice is 5.
(ii)  the difference of the numbers on the two dice is 3.

(Q 28 – 30/2/2 – CBSE 2026 Question Paper)

Ans:

We know that in case of n dice, the total outcomes = (6)ⁿ

∵ here we have 2 dice, ∴ total outcomes = (6)² = 36 outcomes

(i) Sum of the numbers is 5:

To get sum of 5 on a throw of 2 dice, Possible pairs are:

{(1,4), (2,3), (3,2), (4,1)} = 4 outcomes

We know that the Probability is given by:

Probability to get sum of 5, P₅ =

Therefore, the probability to get sum of 5 on throw of two dice =

(ii) Difference of the numbers is 3:

To get difference of 3 on a throw of 2 dice, possible pairs are:

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

We know that the Probability is given by:

Probability to get difference of 3, P₃ =

Therefore, the probability to get difference of 3 on throw of two dice =

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