Exercise · ZW-LAW-OF-TOTAL-PROBABILITY-008 · ★★☆ Intermediate
A die is rolled. On a 6 a ball is drawn from an urn where P(red) is 1/2; otherwise from another where it is 1/10. Probability of drawing red?
Choose one option.
Show answer
- D. 1/6
Explanation
\(\tfrac16\cdot\tfrac12+\tfrac56\cdot\tfrac1{10}=\tfrac1{12}+\tfrac1{12}=\tfrac16\).
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.
\[P(A)=\sum_{i=1}^{n}P(A\mid B_i)\,P(B_i)\]
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