Suppose E, F1, F2 and F3 are events from a sample space S. a) If p(F1)+p(F2 )+p(F3)> 1, is it possible for F1, F2 and F3 to be disjoint? b) Does E = (E∩F1)∪(E∩F2)∪(E∩F3) imply S = F1∪F2∩F3 ? c) Does E = (E∩F1)∪(E∩F2)∪(E∩F3) imply F1, F2 and F3 are pairwise disjoint?

Suppose E, F1, F2 and F3 are events from a sample space S. a) If p(F1)+p(F2 )+p(F3)> 1, is it possible for F1, F2 and F3 to be disjoint? b) Does E = (E∩F1)∪(E∩F2)∪(E∩F3) imply S = F1∪F2∩F3 ? c) Does E = (E∩F1)∪(E∩F2)∪(E∩F3) imply F1, F2 and F3 are pairwise disjoint?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Suppose E, F1, F2 and F3 are events from a sample space S.
a) If p(F1)+p(F2 )+p(F3)> 1, is it possible for F1, F2 and F3 to be disjoint?
b) Does E = (E∩F1)∪(E∩F2)∪(E∩F3) imply S = F1∪F2∩F3 ?
c) Does E = (E∩F1)∪(E∩F2)∪(E∩F3) imply F1, F2 and F3 are pairwise disjoint?

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