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Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having n number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability (Event) = Favourable Outcomes/Total Outcomes =xn
Terms in Probability
Experiment: A trial or an operation conducted to produce an outcome is called an experiment.
Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.
Favourable Outcome: An event that has produced the desired result or expected event is called a favourable outcome. For example, when we roll two dice, the possible/favourable outcomes of getting the sum of numbers on the two dice as 4 are 1, 3, 2, 2 and 3, 1.
Trial: A trial denotes doing a random experiment.
Random Experiment: An experiment that has a well-defined set of outcomes is called a random experiment. For example, when we toss a coin, we know that we would get ahead or tail but we are not sure which one will appear.
Event: The total number of outcomes of a random experiment is called an event.
Equally Likely Events: Events that have the same chances or probability of occurring are called equally likely events. The outcome of one event is independent of the other. For example, when we toss a coin, there are equal chances of getting a head or a tail.
Exhaustive Events: When the set of all outcomes of an experiment is equal to the sample space, we call it an exhaustive event.
Mutually Exclusive Events: Events that cannot happen simultaneously are called mutually exclusive events. For example, the climate can be either hot or cold. We cannot experience the same weather simultaneously.
Basic Theorems on Probability:
Theorem 1
The sum of the probability of happening of an event and not happening of an event is equal to 1. PA+PA = 1
Theorem 2
The probability of an impossible event or the probability of an event not happening is always equal to 0. Pϕ=O.
Theorem 3
The probability of a sure event is always equal to 1. PA=1.
Theorem 4
The probability of happening of any event always lies between 0 and 1.
Theorem 5
If there are two events A and B, we can apply the formula of the union of two sets and we can derive the formula for the probability of happening of event A or event B as follows.
PA∪B=PA+PB-PA∩B
Also for two mutually exclusive events A and B, we have PA∪B=PA+PB
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