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Conditional Probability

If Pnot A=0...

Question

If $P (n o t A) = 0.7, P (B) = 0.7$ and $P (B / A) = 0.5$ , find $P (A ⋃ B)$ .

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Solution

$P (\frac{B}{A}) = \frac{P (A ⋂ B)}{P (A)}$

$0.5 = \frac{P (A ⋂ B)}{0.3}$ \\ $P (A ⋂ B) = 0.15$

$P (\frac{A}{B}) = \frac{P (A ⋂ B)}{P (B)} = \frac{0.15}{0.7} = 0.214$

$P (A ⋃ B) = 0.3 + 0.7 - 0.15 = 0.85$

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