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)

🙏 Thank you all for your time and support! 🙏
Don't forget to catch me daily for the latest updates on my programming journey! Let's continue to learn, grow, and inspire together! 💻✨