Question

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?  that the product of numbers appearing on the top of the dice is less than 9.  

Answer 1

A pair of dice is thrown

TO FIND: Probability of the following:

Let us first write the all possible events that can occur

(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),

Hence total number of events is `6^2=36`

Favourable outcomes for getting the product of numbers less than 9 are
(1, 1), (2, 1), (1, 2), (3, 1), (1, 3), (4, 1), (2, 2), (1, 4), (5, 1), (1, 5), (1, 6), (2, 3), (3, 2), (6, 1), (4, 2), (2, 4)
Thus, the number of favourable outcomes are 16.
∴ P(getting the product of numbers less than 9) =\[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{16}{36} = \frac{4}{9}\]