Exercise · ZW-CONDITIONAL-PROBABILITY-008 · ★★☆ Intermediate
If \(P(A)=0.4\) and \(P(B\mid A)=0.5\), what is \(P(A\cap B)\)?
Choose one option.
Show answer
- A. 0.2
Explanation
Solving the definition, \(P(A\cap B)=P(A)\,P(B\mid A)=0.4\cdot0.5=0.2\). Dividing (0.8) or adding (0.9) is a mistake.
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
- ZW-CONDITIONAL-PROBABILITY-001 If P(A∩ B)=0.2 and P(B)=0.5, what is P(A| B)?
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- ZW-CONDITIONAL-PROBABILITY-003 Two fair dice are rolled and the first shows 3. What is the probability that the sum is 8?
- ZW-CONDITIONAL-PROBABILITY-004 If P(A)=0.6, P(B)=0.4 and P(A∪ B)=0.7, what is P(A| B)?
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- ZW-CONDITIONAL-PROBABILITY-007 A family has two children and at least one is a girl. Assuming each child is equally likely to be a…
- ZW-CONDITIONAL-PROBABILITY-009 With P(B)>0, which statement is true?
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