Probability Basics

Python'da İstatistiksel Benzetim

Tushar Shanker

Data Scientist

Sample Space

Sample Space $S$: Set of all possible outcomes

Dice Sample Space

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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. $P(H) + P(T)=1$
Python'da İstatistiksel Benzetim

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

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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 $B$:
    • $P(A \cap B) = 0$
    • $P(A \cup B) = P(A) + P(B)$
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Probability

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

A Intersection B

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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.
Python'da İstatistiksel Benzetim

Let's practice!

Python'da İstatistiksel Benzetim

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