An experiment is given together with an event Find the model

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost. (Compare with Exercises 1-10 in Section 7.1.)

Two dice are rolled; the numbers add to 7.

Solution

When 2 dice are rolled, Sample space = {(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)} = 36

the numbers add to 7 = { (1,6) , (2,5), (3,4), (4,3), (5,2), (6,1) } = 6

p( the numbers add to 7) = 6/36 = 1/6