Two dice are tossed simultaneously. Find the probability of getting

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 = $\frac{favourable~outcomes}{total~outcomes}$

∴ P (even no. on both dice) = $\frac{9}{36} = \frac{1}{4}$

Therefore, the probability of getting “an even number on both dice” is $\frac{1}{4}$

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 = $\frac{favourable~outcomes}{total~outcomes}$

∴ P (sum of two numbers > 9) = $\frac{6}{36} = \frac{1}{6}$

Therefore, the probability of getting “sum of two numbers more than 9” is $\frac{1}{6}$

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