Probability
Learning Objectives
- Probability
- Playing Cards
Probability
A mathematically measure of uncertainty is known as probability. If there are ‘a’ elementary events associated with a random experiment and 'b' of them are favourable to event 'E';
- Then the probability of occurrence of event E is denoted by P(e).
\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,P(E)=\frac{b}{a}\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,0\le P(E)\le 1\]
- The probability of non-occurrence of event E denoted by P(e) and is defined as \[\frac{a-b}{a}.\]
\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,P(\overline{E})=\frac{a-b}{a}=1-\frac{b}{a}=1-P(E)\]
- \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,P(E)+P(\overline{E})=1\]
Experiment
An operation which can produce some well- defined outcomes is called an experiment.
Random Experiment: An experiment in which all possible outcomes are known and exact outcome cannot be predicted is called a random experiment.
Example: Rolling an unbiased dice has all six outcomes (1, 2, 3, 4, 5, 6) known but exact outcome can be predicted.
Outcome: The result of
more...
