Q) Two dice are tossed simultaneously. Find the probability of getting
(i) an even number on both dice.
(ii) the sum of two numbers more than 9.

Ans:

Step 1: Since each die has 6 faces and we are tossing 2 dice,

∴ Total outcomes = (6)² = 36

Part (i)

Step 2: Let’s first calculate possibilities of getting even numbers on both dice:

The even numbers on any dice are: {2, 4, 6}

Since, an even number on a dice can pair with the even number on other dice,

hence, total favourable outcomes (of getting even number on both dice) are: 3 x 3 = 9

Step 3: ∵ Probability =

∴ P (even no. on both dice) =

Therefore, the probability of getting “an even number on both dice” is

Part (ii):

Step 4: Now let’s calculate possibilities of getting sum on both dice which is greater than 9:

∵ Possible sums greater than 9 are {10, 11, 12}.

Let’s calculate possibilities for each of these sums:

∴ For sum = 10, possibilities are (4,6), (5,5), (6,4) i.e. 3 outcomes

∴ For sum = 11, possibilities are (5,6), (6,5) i.e. 2 outcomes

∴ For sum = 12, possibilities are (6,6) i.e. 1 outcome

∴ Total favorable outcomes = 3 + 2 + 1 = 6

Step 5: ∵ Probability =

∴ P (sum of two numbers > 9) =

Therefore, the probability of getting “sum of two numbers more than 9” is

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