Exercise · ZW-CONDITIONAL-PROBABILITY-001 · ★☆☆ Basic
If \(P(A\cap B)=0.2\) and \(P(B)=0.5\), what is \(P(A\mid B)\)?
Choose one option.
Show answer
- B. 0.4
Explanation
Divide the intersection by the probability of what is known: \(0.2/0.5=0.4\). Multiplying (0.1) or adding (0.7) is not the definition.
Review the concept: Conditional probability
The conditional probability of \(A\) given \(B\), \(P(A\mid B)\), is the probability that \(A\) occurs when \(B\) is already known to have occurred; it is computed within the space reduced to \(B\).
\[P(A\mid B)=\frac{P(A\cap B)}{P(B)},\qquad P(B)>0\]
More practice problems: conditional probability
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