Probability Basics

Statisticale simulatie in Python

Tushar Shanker

Data Scientist

Sample Space

Sample Space $S$: Set of all possible outcomes

Dice Sample Space

Statisticale simulatie in Python

Probability

Sample Space $S$: Set of all possible outcomes

Probability $P(A)$: Likelihood of event $A$

  • $0 \leq P(A) \leq 1$
  • $P(S) = 1$ eg. $P(H) + P(T)=1$
Statisticale simulatie in Python

Probability

Sample Space $S$: Set of all possible outcomes

Probability $P(A)$: Likelihood of event $A$

  • $0 \leq P(A) \leq 1$
  • $P(S) = 1$ eg. $P(H) + P(T)=1$

Coin

Statisticale simulatie in Python

Mutually Exclusive Events

Sample Space $S$: Set of all possible outcomes

Probability $P(A)$: Likelihood of event $A$

  • $0 \leq P(A) \leq 1$
  • $P(S) = 1$
    • $P(H) + P(T)=1$
  • For mutually exclusive events $A$ and $B$:
    • $P(A \cap B) = 0$
    • $P(A \cup B) = P(A) + P(B)$
Statisticale simulatie in Python

Probability

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

A Intersection B

Statisticale simulatie in Python

Using Simulation for Probability Estimation

Steps for Estimating Probability:

  1. Construct sample space or population.
  2. Determine how to simulate one outcome.
  3. Determine rule for success.
  4. Sample repeatedly and count successes.
  5. Calculate frequency of successes as an estimate of probability.
Statisticale simulatie in Python

Let's practice!

Statisticale simulatie in Python

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