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Unit 14: Probability
14.2 Sample Space Notes
Even though we cannot forecast the result of a random experiment with certainty we typically
can state a set of potential outcomes. This provides the first element in our model for a random
experiment.
Definition
The sample space Ù of a random experiment is defined as the set of all achievable results of the
experiment.
Example: of random experiments along with their sample spaces are:
1. Cast two dice successively,
= {(1, 1), (1, 2), . . . , (1, 6), (2, 1), . . . , (6, 6)}.
2. The lifetime of a machine (in days),
= R+ = {positive real numbers} .
3. The number of coming calls at an exchange throughout a specific time interval,
= {0, 1, · · · } = Z+ .
4. The heights of 10 chosen people.
10
= {(x1, . . . , x10), xi e” 0, i = 1, . . . , 10} = R+ .
Here (x1, . . . , x10) displays the result that the length of the first chosen person is x1, the length
of the second person is x2, etc.
Did u know? For modeling purposes it is frequently simpler to take the sample space
larger than needed.
Example: The real lifetime of a machine would surely not extent the whole positive real
axis. And the heights of the 10 chosen people would not surpass 3 metres.
Self Assessment
Fill in the blanks:
4. Even though we cannot forecast the result of a random experiment with certainty we
typically can state a set of potential ............................. .
5. The ............................. of a random experiment is defined as the set of all achievable
results of the experiment.
6. For modeling purposes it is frequently simpler to take the sample space .............................
than needed.
14.3 Events
Frequently we are not concerned in a single result but in whether or not one of a group of results
appears. Such subsets of the sample space are known as events. Events will be signified by
capital letters A,B,C, . . . . We say that event A appears if the result of the experiment is one of the
essentials in A.
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