Statistics
Probability basics
Probability measures how likely an outcome is, on a scale from 0 to 1. Multiply probabilities for events that must both happen; add them for mutually exclusive alternatives, subtracting the overlap when there is one.
Why it matters
Probability is heavily weighted in data-handling exam sections and is the foundation for statistics courses, risk reasoning and later machine-learning study.
Worked example
A bag has 5 red and 3 blue counters. Two are drawn without replacement. P(both red)?
- 1First draw. P(red) = 5/8
- 2Update the bag. 4 red remain of 7 counters
- 3Second draw. P(red | red) = 4/7
- 4Multiply. 5/8 × 4/7 = 20/56
Answer: 5/14 ≈ 0.357
Common mistakes
- Using the same denominator for the second draw when there is no replacement.
- Adding probabilities for events that must both occur.
- Forgetting to subtract the overlap in P(A or B).
How to check your answer
- Every probability must lie between 0 and 1.
- The probabilities of all possible outcomes must sum to 1.
Related topics
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