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Probability Rules
Probability is a branch of mathematics and statistics that studies uncertainty and chance. It measures how likely an event is to occur. It helps us analyze random situations and forms the foundation of statistical inference.
Basic Rules:
We use 𝑃(𝐴) to represent the probability for the event 𝐴 to occur.
Range: 0 ≤ 𝑃(𝐴) ≤ 1, where:
𝑃(𝐴) = 0 means that the event 𝐴 is impossible to occur
P(A) = 1 means the event 𝐴 would certainly occur.
Complement Rule: 𝑃(𝑛𝑜𝑡 𝐴) = 1 − 𝑃(𝐴)
Addition Rule: 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)
Multiplication Rule: 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ⋅ 𝑃(𝐵 ∣ 𝐴)
Conditional Probability: 𝑃(𝐵∣𝐴)=𝑃(𝐴𝑎𝑛𝑑𝐵)𝑃(𝐴)
Mutually Exclusive:
If event A and event B are mutually exclusive, then the two events cannot happen at the same time.
Example Question:
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