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(A ^{c}) = 1∴ P(A ^{c}) = 1 - P(A)
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 Conditional Probability: 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.Independent Events:If A and B are independent events then If A _{1}, A_{2}, A_{3},....,A_{N} are independent events associated with a
random experiment then we can say that Let S be the sample space and ELaw of Total Probability:_{1}, E_{2},
E_{3}...E_{N} are N mutually exclusive and exhaustive events associated with the random experiment. If A is any event that occurs with E_{1}, E_{2},....,E_{N}, then Let S be the sample space and EBaye's Theorm:_{1}, E_{2}, E_{3}
...E_{N} are N mutually exclusive and exhaustive events associated with the random experiment. If A is
any event that occurs with E_{1}, E_{2},....,E_{N}, then## Download: Permutation and Combination: Basic Concept with Examples## Download: Probability: Basic Concept with Examples |