4. Let B be an event such that P{B} > 0. Show that P{ |B} satisfies (1.1),...

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4. Let B be an event such that P{B} > 0. Show that P{· |B} satisfies (1.1), (1.2) and

(1.3), which means to show that

(i) P{A|B} ≥ 0 for all events A.

(ii) P{S|B} = P{B|B} = 1.

(iii) Let AB and CB be disjoint events. Then P{A ∪ C|B} = P{A|B} + P{C|B}.

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