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**Repulsion**. The event

*A*is said to be repelled by the event

*B*is P(A|B) < P(A), and to be attracted by

*B*P(A|B) > P(A).

(a) Show that if

*B*attracts

*A*, then

*A*attracts

*B*, and

*~B*repels

*A*.

(b) If

*A*attracts

*B*, and

*B*attarcts

*C*, does

*A*attract

*C*?

(c) Explain this, throught ratio idea:

P(A|B) > P(A) => P(B|A) > P(B).