Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is
(i) 8? (ii) 13? (iii) less than or equal to 12?
Solution:
Total possible outcomes:
Since each die has 6 sides, the total number of possible outcomes is:
6 × 6 = 36
(i) Event E: Sum = 8
Favourable outcomes:
(2,6), (3,5), (4,4), (5,3), (6,2)
Number of favourable outcomes = 5
P(E) = 53/6
(ii) Event F: Sum = 13
This is impossible since the highest sum with two dice is 6 + 6 = 12.
Number of favourable outcomes = 0
P(F) = 0/36 = 0
(iii) Event G: Sum ≤ 12
Since the maximum sum is 12 (with 6 + 6), all outcomes are favourable.
Number of favourable outcomes = 36
P(G) = 36/36 = 1