Two different dice are thrown together. Find the probability that the numbers obtained

(i) have a sum less than 7

(ii) have a product less than 16

(iii) is a doublet of odd numbers. [CBSE 2017]

Sample space = {(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)}

(i) Numbers obtained on die such that the sum is less than 7 are: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)

∴ Probability that pair has the sum is less than 7 =

(ii) Numbers obtained on die such that the product is less than 16 are: (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), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3), (6, 1), (6, 2)}

No. of pairs obtained such that the product is less than 16 = 25

∴ Probability that the product is less than 16 =

(iii) Doublet of odd numbers means that numbers obtained on the two dice should be both odd.

So, odd doublets obtained are: (1, 1), (1, 3), (1, 5), (3, 1),

(3, 3), (3, 5), (5, 1), (5, 3), (5, 5)

Number of odd doublets = 9

Therefore, Probability of getting an odd doublet =