Exercise · ZW-LAW-OF-TOTAL-PROBABILITY-004 · ★☆☆ Basic
What must a family \(B_1,\dots,B_n\) satisfy to be used in the law of total probability?
Choose one option.
Show answer
- D. Be pairwise disjoint with union equal to the sample space
Explanation
The cases must be mutually exclusive and exhaustive: a partition. Equal probabilities or independence are not needed, and without full coverage probability is lost.
Review the concept: Law of total probability
The total probability of an event \(A\) is the weighted average of its conditional probabilities \(P(A\mid B_i)\) over a partition \(B_i\) of the sample space, with the probability of each case as its weight.
\[P(A)=\sum_{i=1}^{n}P(A\mid B_i)\,P(B_i)\]
More practice problems: law of total probability
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