Probability of an event from its complement, the intersection from the addition rule and a conditional probability
Probability of an event from its complement, the intersection from the addition rule and a conditional probability
6 marks
Two events \(A\) and \(B\) are such that \(P(A)=\frac25\), \(P(B')=\frac14\) and \(P(A\cup B)=\frac78\).
- Write down \(P(B)\).
- Find \(P(A\cap B)\).
- Find \(P(A\mid B)\).
[6]
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Answer:\(P(A\cap B)=\frac25+\frac34-\frac78=\frac{11}{40}\), so \(P(A\mid B)=\frac{11/40}{3/4}=\frac{11}{30}\).
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