Exercise · ZW-LAW-OF-TOTAL-PROBABILITY-005 · ★☆☆ Basic
It rains with probability 0.3. If it rains you are late with probability 0.5; otherwise 0.1. What is the probability that you are late?
Choose one option.
Show answer
- B. 0.22
Explanation
\(0.3\cdot0.5+0.7\cdot0.1=0.15+0.07=0.22\). The 0.15 only counts the rainy case.
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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