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Problem 1. Let A event from outcome space S,equipped with probability function I . Prove that P(A) 1. Hint: You can use theorem 1.4 Problem 2. Let A,B,C events from outcome space S, equipped with probability function P. Prove that P(AUBUC)- P(A)+P(B)+P(C)- PAnB) PAnC) PBnC) +P(AnBnc) Hint: You can treat A and BUC as two events and apply theorem 1.6. You will also need to use Law 5 from the distributive laws.

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et A event om utceme spacesequipped with s nblem 1 Here parnhahiliby afan im passihle esen is 2e Here we lenow that alsoPlA2Aedl e lenau that en From eq = r l (AUB) n (AUC) I prom egno fou m eg P(A)t PC)-P(AAC -P(ANE)+P(ANG AC) The fommula o events

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