Question

If $P\left(A\right)=0.6$ and the greatest value of $P(A\cap B)=0.4$, then the greatest value of $P\left(B\right)$ is $\frac{k}{10}$. The value of $k$ is

Answer 1

We know, $P(A\cup B)\le 1\Rightarrow P\left(A\right)+P\left(B\right)-P(A\cap B)\le 1$
$\therefore P\left(B\right)\le 1-P\left(A\right)+P(A\cap B)\Rightarrow P\left(B\right)\le 1-0.6+0.4\le 0.8$
$\therefore P\left(B\right)\le 0.8=\frac{8}{10}=\frac{k}{10}$
$\Rightarrow k=8$