SUMMARY OF PROBABILITY THEORY
PROBABILITY - 6
Probability theory :-
What is probability ?
Numerical representation of likelihood events.
Numeric values between 0 to 1.
More towards 1 the more likelihood ( occurrence )
Event means which is an outcome of a random experiment.
Probability of event = no.of occurrence ( event ) / no.of occurrence ( sample )
What is a sample ?
It is a total outcome possibility.
Example :-
When we toss, what is the probability of getting head ?
Event is Head. { how many time we can get head in a single toss } = 1
Sample means what we can get from the experiment is { Head , Tail } = 2 outcomes
Probability of getting Head is = 1 / 2 = 0.5
ODDs RATIO :-
OR = PROBABILITY / 1- PROBABILITY
Probability / Probability against the event.
EXAMPLE :-
Getting a head probability is 0.5 ?
The probability of getting odd = 0.5 / 1 - 0.5 = 1
Type of events :-
Independent / dependent.
Mutually exclusive :- cannot be done together.
Type of probability :-
Joint probability :-
A= Getting a head
B = Getting an even number.
P ( A U B) = P(A) * P(B)
Conditional probability :-
A= Getting a even number
B = Getting a number greater than 4..
P ( A | B) = P(A ⋂ B) / P(B) = 1 / 6 / 2 / 6 = 1/2
P ( A | B) = what is the probability of A happening when B already happened.
Bayes Theorem :-
It works on conditional probability .
P ( A | B) = P(A) * P(B | A) / P(B)
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