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# If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find i) P(A ∩ B), (ii) P(A|B) and (iii) P(A ∪ B)

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

i) P(A ∩ B)

(ii) P(A|B)

(iii) P(A ∪ B)

Toolbox:
• $p(B/A)=\frac{P(A\cap\;B)}{P(B)}$
• $P(A\cap\;B)=P(B/A)\;P(A)$
• $also\;P(A\cup\;B)=P(A)+P(B)-P(A\cap\;B)$
• $P(A/B)=\frac{P(A\cap\;B)}{P(B)}$
$P(A)=0.8\;P(B)=0.5\;p(B/A)=0.4$
$P(A\cap\;B)=0.4x0.5$
$0.32$
$P(A/B)=\frac{P(A\cap\;B)}{p(B)}$
=$\frac{0.32}{0.5}\frac{32}{50}=0.64$
$p(A\cup\;B)=0.8+0.5-0.32$
=$0.98$