Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is :
(i) 4 or 5
(ii) 7, 8 or 9.
(iii) between 5 and 8.
(iv) more than 10.
(v) less than 6.

Question

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is :
(i) 4 or 5
(ii) 7, 8 or 9.
(iii) between 5 and 8.
(iv) more than 10.
(v) less than 6.

KnowledgeBoat · Accepted Answer

When two dice are rolled together; No. of possible outcomes = 6 × 6 = 36. (i) Favourable outcomes for sum of numbers on the upper-most faces of two dice to be 4 or 5 are : (1, 3), (1, 4), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1). ∴ No. of favourable outcomes = 7. P(getting a sum of 4 or 5) = . Hence, the probability of getting sum of numbers on the upper-most faces of two dice to be 4 or 5 = . (ii) Favourable outcomes for sum of numbers on the upper-most faces of two dice to be 7, 8 or 9 are : (1, 6), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 3), (4, 4), (4, 5), (5, 2), (5, 3), (5, 4), (6, 1), (6, 2) and (6, 3). ∴ No. of favourable outcomes = 15. P(getting a sum of 7, 8 or 9) = . Hence, the probability of getting sum of numbers on the upper-most faces of two dice to be 7, 8 or 9 = . (iii) Favourable outcomes for sum of numbers on the upper-most faces of two dice to be between 5 and 8 are : (1, 5), (1, 6), (2, 4), (2, 5), (3, 3), (3, 4), (4, 2), (4, 3), (5, 1), (5, 2), (6, 1). ∴ No. of favourable outcomes = 11. P(getting a sum between 5 and 8) = . Hence, the probability of getting sum of numbers on the upper-most faces of two dice between 5 and 8 = . (iv) Favourable outcomes for sum of numbers on the upper-most faces of two dice to be more than 10 are : (5, 6), (6, 5), (6, 6) ∴ No. of favourable outcomes = 3. P(getting a sum of more than 10) = . Hence, the probability of getting sum of numbers on the upper-most faces of more than 10 = . (v) Favourable outcomes for sum of numbers on the upper-most faces of two dice to be less than 6 are : (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1). ∴ No. of favourable outcomes = 10. P(getting a sum of less than 6) = . Hence, the probability of getting sum of numbers on the upper-most faces of less than 6 = .

Mathematics

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is :
(i) 4 or 5
(ii) 7, 8 or 9.
(iii) between 5 and 8.
(iv) more than 10.
(v) less than 6.

Probability

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Mathematics

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is :(i) 4 or 5(ii) 7, 8 or 9.(iii) between 5 and 8.(iv) more than 10.(v) less than 6.

Probability

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