Question

If \(P(A)=0.8,\ P(B)=0.5\) and \(P(B\mid A)=0.4\), find \(P(A\cup B)\).

Hint:

Get P(A∩B) from P(B|A)·P(A), then use the addition rule.

Answer 1

Step 1: Finding the intersection:
\(P(B\mid A)=\dfrac{P(A\cap B)}{P(A)}\Rightarrow P(A\cap B)=P(B\mid A)\cdot P(A)=0.4\times0.8=0.32\).

Step 2: Applying the addition rule:
\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).

Step 3: Substituting values:
\(P(A\cup B)=0.8+0.5-0.32\).

Final Answer:
\[ \boxed{P(A\cup B)=0.98} \]