Textbook ExpertVerified Tutor
25 Oct 2021
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
Step 1.
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.
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