Question
P(A) = 9/20 P(B|A) = 3/10 P(A and B ) = ?
Answer
$$ P(A \text{ and } B) = \dfrac{ 27 }{ 200 } $$
Explanation
To find $ P(A \text{ and } B) $ we use multiplication rule:
$$ \color{blue}{P(B ~|~ A) = \frac{ P(A \text{ and } B)}{P(A)}} $$In this example we have:
$$ \begin{aligned} P(B ~|~ A) &= \frac{ P(A \text{ and } B)}{P(A)} \\ \frac{ 3 }{ 10 } &= \frac{ P(A \text{ and } B)}{ \frac{ 9 }{ 20 } } \\ P(A \text{ and } B) &= \frac{ 3 }{ 10 } \cdot \frac{ 9 }{ 20 } \\ P(A \text{ and } B) &= \frac{ 27 }{ 200 } \end{aligned}$$This page was created using
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