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4.13. Generalize Exercise 1.2.5 to obtain say that C1,Ca, ,Ck are independent events that have respective probabilities Pi,P. Pk Argue that the probability of at least one of C1, C2, , Ck is equal to 1-(1-P)(1-pa)(1-P) -p1) (1- p2):..
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Probability of at least one of C1, C2, .., Ck P(C1 UC2 U... UCk) P(Ci n 2 n . n) Using DeMorgans law 1-P (C) P(C) P(C k), snce cis are ndependent Cİ are also n dependen t since P(C) = pi, î = 1.2, k- P(C) = 1-P(C) = 1-Pi, i = 1, 2, , k.

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