Exercise · ZW-LAW-OF-TOTAL-PROBABILITY-002 · ★☆☆ Basic
Urn A has 3 red and 2 blue balls; urn B has 1 red and 4 blue. A fair coin picks an urn and a ball is drawn. What is the probability that it is red?
Choose one option.
Show answer
- C. 2/5
Explanation
\(\tfrac12\cdot\tfrac35+\tfrac12\cdot\tfrac15=\tfrac25\). Adding the two conditionals without weights would give 4/5.
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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