Does the compound event consist of two mutually exclusive events? Two dice are rolled. The sum of the dice is a 5 or a 6. Compute the probability of the compound event occurring.

Answer 1

A compound event consists of two individual events.

Mutually exclusive events are events that cannot occur at the same time. The events of rolling a 6 with a die and a 5 with a die on the same roll cannot occur at the same time.

Here is a table of possible sums of the roll of two die. The values for Die 1 and Die 2 are along the side and top. The sums are in the middle. For example the sum of Die 1 = 2 and Die 2 = 2 is 4.

Die 2

Die 1 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

There are 6 * 6 = 36 possible outcomes to rolling two die, 36 possible sums. The number of events in the sample space are 36.

Looking at the table a 5 or a 6 occurs as the sum 9 times, so 9 of the 36 possible events are the event where the sum is 5 or 6.

probability = number of occurrents of desired events/number of events in sample space = 9/36 = 1/4