Page 206 - DMTH202_BASIC_MATHEMATICS_II

Unit 14: Probability

Self Assessment Notes

Fill in the blanks:
12. Probability informs us how .......................... it is that a specific event will take place.
13. A probability rule P has precisely the .......................... properties as the general “area
measure”.
14. To discover the probability of the set A we have to sum up the .......................... of all the
essentials in A.

15. When the sample space is not countable, it is supposed to be .......................... .

14.5 Summary

 A probability is a mathematical measure of the possibility of the event.
 The fundamental view in probability is that of a random experiment: an experiment
whose result cannot be revealed beforehand, but is however still dependent on analysis.
 Even though we cannot forecast the result of a random experiment with certainty we
typically can state a set of potential outcomes.
 The sample space  of a random experiment is defined as the set of all achievable results
of the experiment.
 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.
 Two events A and B which have no results in general, that is, A  B = , are known as
disjoint events.
 The third element in the model for a random experiment is the requirement of the
probability of the events. It informs us how likely it is that a specific event will take place.
 The issue of what probability actually is does not have a completely acceptable answer. In
some conditions it may be supportive to consider probability as displaying long-run
amount or degree of belief.

14.6 Keywords

Disjoint Events: Two events A and B which have no results in general, that is, A  B = , are
known as disjoint events.
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.
Probability: A probability is a mathematical measure of the possibility of the event.
Random Experiment: The fundamental view in probability is that of a random experiment: an
experiment whose result cannot be revealed beforehand, but is however still dependent on analysis.
Sample Space: The sample space Ù of a random experiment is defined as the set of all achievable
results of the experiment.

14.7 Review Questions

1. Illustrate the concept of random experiments with examples.
2. A die is rolled, find the probability that an even number is obtained.

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