Q) Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that:
(i) same number appears on both the dice?
(ii) different number appears on both the dice?

(Q 31 – 30/1/1 – CBSE 2026 Question Paper)

Ans:

Step 1: We know that in case of n dice, the total outcomes = (6)ⁿ

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

It will have following combinations = {(1,1), (1,2), (1,3), ….. , (6,6)}

(where first number = outcome of die 1, second = outcome of die 2)

(i) Probability to get same number on both dice: 

Step 2: ∵ when both dice will show same numbers, then outcomes = (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

∴ Favourable outcomes to have same numbers on both dice = 6 outcomes

Step 3: We know that the Probability is given by:

Probability to get even sum, P_{Same No.}=

Therefore, the probability to get same number on two dice =

(i) Probability to get different number on both dice: 

Step 4: ∵ when both dice will show different numbers, then outcomes:

= total outcomes – outcomes for same numbers

= 36 – 6 = 30 outcomes

∴ Favourable outcomes to have different numbers on both dice = 30 outcomes

Step 5: We know that the Probability is given by:

Probability to get diffeent number, P_{Diff No.}=

Therefore, the probability to get different number on two dice =

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