Question

Two different dice are rolled simultaneously. Find the probability that the sum of numbers appearing on the two dice is 10 ?

Answer 1

The first die could show any one of the numbers 1, 2, 3, 4, 5, 6. The same is true for the second die as well.

The possible outcomes 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), (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)}

\[\therefore\] Number of possible outcomes =\[6 \times 6 = 36\]

 

Let E be the event that the sum of numbers appearing on the two dice is 10.
The outcomes favourable to event, E are {(4, 6), (5, 5), (6, 4)}.
∴ Number of outcomes favourable to event, E = 3

\[P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} = \frac{3}{36} = \frac{1}{12}\]