Probability Rules

rules for probability

𝑃 (A ∪ B)

𝑃 (A) + 𝑃( B) − 𝑃( A ∩ B)

𝑃 𝐴 ∩ 𝐵 =

𝑃(A) ∙ 𝑃 (B/A) or 𝑃(B) ∙ 𝑃 (A/B)

When multiplicative rule used

When A given B or B given A is known

When conditional prob. rule used

When intersection is known

Collectively exhaustive

if at least one event must occur

Compound events occur

union or intersection

𝑃 (𝐴 l 𝐵)=

𝑃(𝐴 ∩ 𝐵) / 𝑃 (B) 

𝑃 (B l A)=

𝑃(𝐴 ∩ 𝐵)/ 𝑃 (A)