PROBABILITY RULE COPIED! 🎲

Probability Rule 🎲

P(A) =
n(E)
n(S)
0 P(A) 1
Concept: Desired outcomes divided by the total number of possible outcomes.

Probability Mastery Guide 🎲

ε
Experiment

An action or process that leads to an observable result (like rolling a die).

S
Sample Space

The set of all possible outcomes of an experiment. For a die, S = {1, 2, 3, 4, 5, 6}.

E
The Event

A specific outcome or a set of outcomes we are interested in from the Sample Space.

A ∩ B = ∅
Mutually Exclusive

Events that cannot happen at the same time. If one happens, the other cannot.

P(A|B)
Independent

When the occurrence of one event does not affect the probability of another event.

P(A')
Complement

The probability of an event NOT happening. Calculated as 1 - P(A).

0
Impossible

An event that can never happen has a probability of exactly 0.

1
Certain Event

An event that is 100% guaranteed to happen has a probability of exactly 1.

P(A|B)
Conditional

The probability of event A happening, given that event B has already occurred.

Legacy of Probability 🎲

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1654 | THE GAMBLER'S PROBLEM

It all started with a gambler named Chevalier de Méré. He asked Blaise Pascal how to divide the prize money in an unfinished game, leading to the birth of modern Probability.

PASCAL & FERMAT

Blaise Pascal and Pierre de Fermat exchanged a series of letters to solve gambling problems. Together, they laid the mathematical foundation for calculating chances.

1812 | PIERRE-SIMON LAPLACE

Laplace published 'Théorie Analytique des Probabilités', moving it beyond gambling. He applied probability to science and everyday life, calling it "common sense reduced to calculation."

"Did you know? In 1713, Jacob Bernoulli proved the 'Law of Large Numbers', showing that the more times you repeat an experiment (like flipping a coin), the closer you get to the true probability!"