Paper 2, Section I, F

Probability | Part IA, 2015

Let A,BA, B be events in the sample space Ω\Omega such that 0<P(A)<10<P(A)<1 and 0<P(B)<10<P(B)<1. The event BB is said to attract AA if the conditional probability P(AB)P(A \mid B) is greater than P(A)P(A), otherwise it is said that AA repels BB. Show that if BB attracts AA, then AA attracts BB. Does Bc=Ω\BB^{c}=\Omega \backslash B repel A?A ?

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