PROBABILITY - 5

BINOMIAL PROBABILITY

Bernoulli trials :-
A random experiment repeated n-times is said to be bernoulli trial if

Trails are independent of each other.
Only two possible outcomes corresponding to each trial, that is success or failure.
Probability of success ( or failure ) in each trial must be the same.

Experiment : a dice is rolled ten times.

Success : occurrence of a number divisible by “3”.

P = prob. Of success in one trial = 1 / 3
Q = prob. Of failure in one trial = 2 / 3

Probability of exactly 4 times success = 10 C 4

Bayes Theorem.

It is a theorem in which we find the probability of an event after the event is completed / happened.
It is derived from the conditional probaility.

Outcome is known before knowing the probability.

P( A|B ) = P( A ) x P( B|A ) / P( B )

Example :-

If a person is dead then baye will ask what is the probability of that person who died having any life-style disease.

Another example :-

We have data of Gender and whether they survived or not and from that with the help of baye we can find out if a man enters what will be the probability that he will survive or not.

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