If \( P(A)=0.4 \), \( P(B)=X \) and \( P(\bar{A}\cap\bar{B})=0.4 \), where A and B are independent event, then the value of X is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1/3
If A and B are independent, their complements are also independent, so
\( \displaystyle P(\bar{A}\cap\bar{B})=P(\bar{A})\,P(\bar{B}) \)
\( \displaystyle =(1-0.4)(1-X) \)
This equals 0.4, so
\( \displaystyle 0.6\,(1-X)=0.4 \)
\( \displaystyle 1-X=\frac{2}{3} \)
\( \displaystyle X=\frac{1}{3} \)