Question

Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.

Answer 1

Given: A pair of dice is thrown

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 6² = 36

Favorable events i.e. getting the total of numbers on the dice greater than 10 is (5, 6), (6, 5) and (6, 6)

So, total number of favorable events i.e. getting the total of numbers on the dice greater than 10 is 3

We know that;

Probability = $\frac{Numberoffavorableevent}{Totalnumberofevent}$

Hence, probability of getting the total of numbers on the dice greater than 10 is $\frac{3}{36}$ =$\frac{1}{12}$