Problem 86f

Given information

Roll two fair dice separately. Each die has six faces.

Let  be the event that either a three or four is rolled first, followed by even number. Let  be the event that sum of the two rolls is at most seven.

Step-by-step explanation

Since two fair dice are rolled the sample space is given by:

,

.

is the event that either a three or four is rolled first, followed by even number. Therefore,

,

.

be the event that sum of the two rolls is at most seven. Therefore,

,

.

The set of event that both the events happen simultaneously is:

,

.

The following formula is used to find the probability of happening event given that happens.

,

It is clear that,

Observe that,

.

Therefore, the events and are not independant.