You roll 2 dice. Find P (even number on one die and 1 on the other).

Each
die has 6 sides, each of them has the same probability to show itself (of course, this
probability is 1/6). There are 3 even numbers on each die, 2, 4 and 6. Also, the outcome of the
second die does not depend on the outcome of the first one.

There are two
disjoint possibilities to get the desired outcome: 1) 1 on the first die and 2, 4 or 6 on the
second and 2) 1 on the second die and 2, 4 or 6 on the first.

Each of these
disjoint events has the same probability of `( 1 / 6 ) * ( 3 / 6 ) = 1 / 12`(we multiply 1/6 and
3/6 because those events are independent). Now we have to add 1/12 and 1/12 because these two
events are disjoint. This way, the final answer is 1/6.

Another way is to count how many outcomes are suitable out of 36 possible: (1,2),
(1,4), (1,6), (2,1), (4,1), (6,1): 6 of 36, i.e. 1/6 again.