Let P(A) = 0.4, P(B) = k, P(A ∪ B) = 0.6. If A and B are independent events, then the value of \'k\' is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1/3
For independent events \( P(A\cap B)=P(A)\,P(B) \). Putting this into the addition rule:
\( \displaystyle P(A\cup B)=P(A)+P(B)-P(A)\,P(B) \)
\( \displaystyle 0.6=0.4+k-0.4k \)
\( \displaystyle 0.6=0.4+0.6k \)
\( \displaystyle k=\frac{0.2}{0.6}=\frac{1}{3} \)
Shortcut: For independent events \( P(A\cup B)=1-P(A')\,P(B') \): here \( 0.4=0.6(1-k) \) gives k = 1/3 at once.