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E-TRADE TOGETHER GLOBAL ACADEMY

Probability

Level 3 · Probability & Statistics · Prerequisite: Course 1.1

ACADEMICALLY APPROVED · DESKTOP RUNTIME VERIFIED · MOBILE QA ENVIRONMENT BLOCKED

9 canonical classes · 4 laboratories · 4 module assessments · project · final assessment

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No payment, enrollment or prerequisite restriction. Review content is available only to authorized administrators.

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MODULE 1

Probability Foundations

Model experiments, events, conditional probability and Bayesian updating.

3.1.1

Random experiments and sample spaces

Learning objectives

  • Define experiment, outcome, sample space, and event
  • enumerate finite spaces without double counting
  • distinguish a model from observations.

Worked examples

Worked example 1

Two ordered coin tosses: Ω={HH,HT,TH,TT}; exactly one head is {HT,TH}, so under a fair independent model P=2/4=1/2.

Worked example 2

Sum of two fair dice is not uniform: sum 2 has one ordered pair, sum 7 has six, so probabilities 1/36 and 6/36.

Common mistake and counterexample

“Six possible sums means each has probability 1/11” confuses distinct values with equally likely elementary outcomes.

Knowledge check and mastery evidence

4/4: define Ω/event, enumerate an ordered space, calculate a complement, and state assumptions; assumption statement mandatory. Connects to event algebra.