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Risk (probability) vs odds

a = disease, b = no disease

Risk vs odds in a common disease:

a = 50 a+b = 100

Risk = 50/100 = 0.5

Odds = 50/50 = 1

Risk vs odds in a rare disease:

a = 1 a+b = 100

Risk = 1/100 = 0.010101

Odds = 1/99 = 0.010000