5 A In Class It Was Shown That For Two Events A And B P Aub P A P B P Anb From This Argue That P Aub P A P 1 (39.75 KiB) Viewed 233 times
a and b, please!!
5. a) In class it was shown that for two events A and B, P(AUB) = P(A)+P(B)- P(ANB). From this, argue that P(AUB) P(A)+P(B). You should use only the three probability axioms given in class and not a Venn diagram to derive this result. b) Given the three events A, B, and C, show that P(AUBUC)<P(A)+P(B)+P(C) using part (a). (Hint: Let D= A U B.) Note that this result can be extended even more generally to Boole's inequality, which states that P(U1=1 A;) < 1=1 P(Aį).
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!