Total Probability using Law of Total Probability
Probability Theory DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding the Law of Total Probability, Law of Total Probability, Bayesian Prior distribution, Weighted Averages, Summation notation implementation, Floating point precision handling, Probability Theory, Statistical Inference, Mathematical Foundations, Set Theory, Data Analysis, Conditional Probability, Sample Space Partitioning, Mutually Exclusive Events, Collectively Exhaustive Events, Marginal Probability.
Given a list of probabilities for a set of mutually exclusive and collectively exhaustive partitions P(Ai) and a list of conditional probabilities P(B|Ai), calculate the total probability P(B) using the Law of Total Probability: P(B) = Σ P(B|Ai) P(Ai).