Consider the events A1, A2,, An defined in a sample space . Show that the probability that
Question:
Consider the events A1, A2,…, An defined in a sample space Ω. Show that the probability that none of them appear is equal to
where S1, S2,…, Sn are the sums defined earlier in Proposition 1.10, and S0 = 1.
Application: For n = 3 assume that P(Ai) = 1∕3 for i = 1, 2, 3. Moreover, assume that P(AiAj) = 1∕9 for any i ≠ j, and P(A1A2A3) = 1∕27. Then, show that P(A′
1A′
2A′
3) = P(A′
1)P(A′
2)P(A′
3).
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Related Book For
Introduction To Probability Volume 2
ISBN: 9781118123331
1st Edition
Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
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