Probability — GL

“The only way to earn out of a Casino is, Own it”

Academic Grounds

Coins

Dice

Cards

Cohort with Red Balls and Green Balls

(Life is not a Game, we don’t know the rules, we don’t the odds, we don’t know the boundaries, and we neither don’t

know the incentives nor its pit falls)

Real life Grounds

What are the odds, I would win the Lottery

What are the odds, I would get Swine flu

What are the odds, I would get a Genetic disorder

What are the odds, it would rain tomorrow

What are the odds, my flight would get fired mid-air

Applications of Probability

Insurance

Risk Management

Computer Game Design

Casino

Data Science

Google Pay Scratch Cards

Welcome to Set Theory

9 shades of P

Monty Hall Game (link)

Probability Calculator( link)

Permutations and Combinations

Frequentist Vs Bayesian

Computation (Complementary, Multiplication and Additional)

How probability plays key role in building models?

Inferential Stats

Hypothesis testing

Null Hypothesis Vs Alternate Hypothesis

Wolfram Examples

Binomial Vs Poisson

Probability Definition

Probability Mind Map (Source: CourseMojo)

Three Properties of Probability

1. 0 ≤ P(A) ≤ 1
2. P(S) = 1
3. P (A ∪ B) = P(A) + P(B)

Example:

Imagine picking a number between 1 to 10 and what is the probability of picking an even number and a number between 1 and 5 ?

P(x is even and x < = 5)
 = P(x is even given x <= 5) P(x <=5)
 = 2/5 * 1/2
 = 1/5

Probability of A or B

P (A ∪ B) = P(A) + P(B) - P (A ∩ B)
P (A or B) = P(A) + P(B) - P(A and B)

Working on the same example…

Imagine picking a number between 1 to 10 and what is the probability of picking an even number or a number between 1 and 5 ?

P(x is even or x <= 5)
  = P(x is even) + P(x <= 5) - P(x is even and x <= 5)
  = 1/2 + 1/2 - 1/5
  = 4/5

Independent Events

If A and B are independent , that is one happening tells you nothing about the other happening

P (A and B) = P(A) * P(B)

Mutual Exclusivity

If A and B are Mutually Exclusive, that means if one happens, the other cannot happen

P (A or B) = P(A) + P(B)
P ( A and B) = 0

Permutations and Combinations

OCDs hate ncr

Women love npr