Question

If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find:

1. P(A∩B)
2. P(A|B)
3. P(A∪B)

Answer 1

$(i)$ $P(A∩B) = P(B|A).P(A)$

$P(A∩B = 0.4\times0.8$

$P(A∩B) = 0.3$

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$(ii)$ $P(A|B)=\frac {P(A∩B)}{P(B)}$

$P(A|B)=\frac {0.32}{0.50}$

$P(A|B)=\frac {32}{50}$

$P(A|B)=0.64$

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$(iii)$ $P(A∪B)=P(A)+P(B)-P(A∩B)$

$P(A∪B)=0.8+0.5 – 0.32$

$P(A∪B)= 0.98$