Chapter 15

Probability

Experiment: It is a situation involving chance or a probability that leads to output (result) called outcomes.

Outcomes: It is the result of a trial experiment or other situation involving uncertainty.

Event: The set of all possible outcomes is called an event.

Compound Event: An event associated to a random experiment is a compound event, if it is obtained by combining two or more elementary events associated to the random experiment.

Occurrence of an Event: An event E associated to a random experiment occurs, if any one of the elementary event associated to the event E is an outcome.

Sample Space: Sample Space is a set of all possible outcomes of an experiment.

Probability of an event: The probability of event E is the number of ways when event E can occur divided by the total number of possible outcomes and it is generally written as P (E) and defined as

Sum of the probability: If events E & F cannot occur simultaneously, then the probability that either E or F occurs is [P (E) + P (F)] and generally, the sum of the probabilities of all the elementary event of an experiment is 1.

Complement of an Event: If event (E), with probability P (E), then probability does not occur is 1 – P (E).

And, generally, we denote as

Here, Event = not E or complement of E

Impossible Event: The probability of an event which is impossible to occur is 0. Also, such an event is called an impossible event.

i.e. P (E) = 0

Sure (certain) Event: The probability of an event which has 100% probability of occurring.

i.e. P (sure event) = 1

Or P (S) = 1, S = sure event.

Equality Likely Event: When there is a 50% chance of rain i.e. there a chance that it might rain but it is also possible that it might not rain. Since, these chances are the same so the event is equally likely to happen.