# Probability

## Probability is a measure of the possibility that an event will occur. Elementary Event An event having only one outcome of the experiment is called an elementary event. Equally Likely outcomes If the probability of all outcomes of an experiment are equal, they are called equally likely outcomes. Experimental Probability Experimental probability or empirical probability is the probability of an event based on what has actually happened. It is the ratio of the number of the trials in which an event is happened to the total number of trials of the experiment. Theoretical Approach to Probability The theoretical probability (also called classical probability) of an event E, P(E), is defined as, Where we assume that the outcomes of the experiment are equally likely. Theoretical probability enables us to predict what would happen without actually performing the experiment. Probability of an Event It is the likelihood or chance that an event will occur. It is defined as, where we assume that the outcomes of the experiment are equally likely. Some Properties • The sum of the probabilities of all the elementary events of an experiment is 1. • Probability of an event E, P(E), always satisfies the following property: Complementary Events If an event E occurs with probability P(E), then the probability with which it does not occur is 1 – P(E). Generally, it is denoted as and Sure Event If an event is sure to occur, its probability is 1. Such an event is called a sure event or a certain event. Impossible Event If an event is impossible to occur, its probability is 0. Such an event is called an impossible event.

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