Intro to Probability

It’s easy but always confusing if you haven’t yet totally understood it in the first place.

The very first thing to do for solving a probability problem, is to CATEGORISE the problem and apply different formula.

• Single Event
• Single Event Repeats
• Independent Events in Sequence

Single Event

• The probability of an event can only be 0 to 1 (or 0% to 100%).
• The probability of event A is often written as P(A).
• The probability of an event with condition is often written as P(condition).

Common cases:

• Flip a coin: P(head) = 1/2.
• Roll a die: P(>3) = 3/6

Theoretical & experimental probabilities

The formula Fav outcomes / Total outcomes only gives you the Theoretical probability.
But when you do some experiments, like flip a coin 10,000 times,
and you may find out the probability of the result of experiments is way so different than the theoretical one.

Single Event Repeats

It’s asking for

Example: Roll a die 100 times, how many times will you get a number greater than 3?
Answer: P(>3) = 3/6 *100
The probability is 50 times.

Multiple Events

Independent events in sequence

A & B happening

Independency

To understand probability, we really need to differentiate independent eventsand dependent events.

Khan lecture: Compound probability of independent events.

Coin flips are INDEPENDENT events:
What happens in the first flip in no way affects what happens in the second flip.

And this is actually one thing that many people don’t realise.

Gambler's Fallacy

There’s someone who thinks, if he got a bunch of heads in a row, then all of a sudden, it becomes more likely on the next flip to get a tails.

THAT IS NOT THE CASE.

Every flip is an independent event. What happened in the past in these flips does not affect the probabilities going forward.

Sample Space

A dummy method, just to draw a table or a tree shows every outcome it could be, and pick out all favourable results.

Refer to Wiki: Sample Space
Refer to article: Sample Space Examples and The Counting Principle

The sample space of an experiment is all the possible outcomes for that experiment.

(Rolling Two dice)

(52 card deck)

Sample Size

It’s also called the Size of Sample Space.

Simply to MULTIPLY.

The Fundamental Counting Principle: If there are a ways for one event to happen, and b ways for a second event to happen, then there are a * b ways for both events to happen.

Sample problem: If shoes come in 6 styles with 3 possible colors, how many varieties of shoes are there?
All you need to do is multiply: 6 • 3 = 18 possible varieties of shoes.

Example:

First to notice that, it’s ONE event.

Example:

Example:

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