high School⏱ 4 min

Conditional Probability

P(A|B) - probability given condition

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ABA∩BP(A)=0.40P(B)=0.50P(A∩B)=0.20
P(A)=0.40
P(B)=0.50
P(A∩B)=0.20
P(B∣A)=P(A∩B)P(A)=0.200.40=0.500P(B|A) = \frac{P(A\cap B)}{P(A)} = \frac{0.20}{0.40} = 0.500

P(A|B) = 0.400

P(B|A) = "probability of B given A occurred" = intersection divided by P(A). Venn diagram: look only inside circle A – what fraction also lies in B?