## Probability: Basic Concept and Important Formulas

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## Basic formulas for Probability

Sample Space: The set of all possible outcomes of a random experiment is known as the sample space.

Event: A subset of the sample space associated with the random experiment is known as an event.

Mutually Exclusive Events: Two or more events are known as mutually exclusive events if the occurance of one of them prevents the occurance of the all others.

Probability of occurrence of any event is defined as the number of cases favorable to an event to the total number of cases.
Let P(A) be the probability of occurrence of event A
Then we can say that Probability of occurrence of any event is always greater than or equal to 0 and less than or equal to 1 i.e. minimum value of probability of event A is 0 and maximum value of probability of event A is 1.

P(A) = 0 indicates an impossible event.
Example: Probability of getting 7 on a dice. We know that we cannot get 7 on a dice therefore this is an impossible event.
P(A) = 1 indicates a sure shot event.
Example: Probability of getting a number greater than 0 and less than 7 on a dice. We know that whenever a dice is tossed we will get a number between 1 and 6 (where 1 and 6 are both included) therefore this is a sure shot event.

As P(A) + P(Ac) = 1
∴ P(Ac) = 1 - P(A)

#### Conditional Probability:

Let us consider two events A and B associated with a random experiment. Then the probability of occurance of event A under the condition that event B has already occured such that P(B)≠0 is known as conditional probability and is dentoed by #### Independent Events:

Events A and B are said to be independent if occurance of event A does not affect the probability of occurance or non-occurance of event B and vice-versa.
If A and B are independent events then If A1, A2, A3,....,AN are independent events associated with a random experiment then we can say that #### Law of Total Probability:

Let S be the sample space and E1, E2, E3...EN are N mutually exclusive and exhaustive events associated with the random experiment. If A is any event that occurs with E1, E2,....,EN, then #### Baye's Theorm:

Let S be the sample space and E1, E2, E3 ...EN are N mutually exclusive and exhaustive events associated with the random experiment. If A is any event that occurs with E1, E2,....,EN, then 