Paper 2, Section I, F

Let $A, B$ be events in the sample space $\Omega$ such that $0<P(A)<1$ and $0<P(B)<1$. The event $B$ is said to attract $A$ if the conditional probability $P(A \mid B)$ is greater than $P(A)$, otherwise it is said that $A$ repels $B$. Show that if $B$ attracts $A$, then $A$ attracts $B$. Does $B^{c}=\Omega \backslash B$ repel $A ?$

*Typos? Please submit corrections to this page on GitHub.*