Two dice are thrown at the same time. Write down all the possible outcomes. Find the probability of getting the sum of two numbers appearing on the top of the dice as :
(i) 13
(ii) less than 13
(iii) 10
(iv) less than 10

Question

Two dice are thrown at the same time. Write down all the possible outcomes. Find the probability of getting the sum of two numbers appearing on the top of the dice as :
(i) 13
(ii) less than 13
(iii) 10
(iv) less than 10

KnowledgeBoat · Accepted Answer

When two dice are thrown, simultaneously.

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

No. of possible outcomes = 6 × 6 = 36.

(i) Favourable outcomes for getting a sum of 13 = 0.

∴ No. of favourable outcomes = 0

P(getting a sum of 13) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{0}{36}$ = 0.

Hence, probability of getting a sum of 13 = 0.

(ii) Favourable outcomes for getting a sum less than 13 = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}.

∴ No. of favourable outcomes = 36

P(getting a sum less than 13) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{36}{36}$ = 1.

Hence, probability of getting a sum less than 13 = 1.

(iii) Favourable outcomes for getting a sum of 10 = {(4, 6), (5, 5), (6, 4)}.

∴ No. of favourable outcomes = 3

P(getting a sum of 10) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{36} = \dfrac{1}{12}$ .

Hence, probability of getting a sum of 10 = $\dfrac{1}{12}$ .

(iv) Favourable outcomes for getting a sum less than 10 = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (6, 1), (6, 2), (6, 3)}.

∴ No. of favourable outcomes = 30

P(getting a sum less than 10) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{30}{36} = \dfrac{5}{6}$ .

Hence, probability of getting a sum less than 10 = $\dfrac{5}{6}$ .

Mathematics

Two dice are thrown at the same time. Write down all the possible outcomes. Find the probability of getting the sum of two numbers appearing on the top of the dice as :
(i) 13
(ii) less than 13
(iii) 10
(iv) less than 10

Probability

Answer

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