Question

Two different dice are thrown together. Find the probability that
(i) the sum of the numbers appeared is less than 7. [CBSE 2011]
(ii) the product of the numbers appeared is less than 18. [CBSE 2017]

Answer 1

Total number of possible outcomes is 36.
(i) The favorable outcomes for sum of numbers on dices 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).
P(the sum of numbers appeared is less than 7)=$\frac{15}{36}=\frac{5}{12}.$

(ii) The favorable outcomes for product of numbers on dices less than 18 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), (4,4), (5,1), (5,2), (5,3), (6,1), (6,2).
P(the product of numbers appeared is less than 18)=$\frac{26}{36}=\frac{13}{18}.$