AI engineering glossary · Probability
What is law of total probability?
Law of total probability: If events B1, B2, ... form a partition of the sample space, the probability of any event A is the sum over i of P(A | Bi) x P(Bi). It lets you compute an overall probability by averaging over separate cases.
Law of total probability: an example
If 60% of orders come from mobile with 4% return rate and 40% from web with 2%, overall return probability = 0.6 x 0.04 + 0.4 x 0.02 = 0.032.
Related terms
More Probability terms
- Likelihood
- Linearity of expectation
- Marginal distribution
- Marginal probability
- Markov chain
- Markov chain Monte Carlo
- Markov property
- Markov's inequality
Where you learn it
Law of total probability is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.