Exercise · ZW-LAW-OF-TOTAL-PROBABILITY-007 · ★★☆ Intermediate
Given \(P(A)=0.5\), \(P(B)=0.5\) and \(P(A\mid B)=0.8\), what is \(P(A\mid B^c)\)?
Choose one option.
Show answer
- A. 0.2
Explanation
\(0.5=0.8\cdot0.5+P(A\mid B^c)\cdot0.5\), so \(P(A\mid B^c)=0.1/0.5=0.2\).
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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