Let A and B be events in sample space having positive probability. (a) If P(A|B) < P(A), show that P(B|A) < P(B). (b) If A ∩ B = ∅, what is P(B|A)? (c) If A ⊆ B, how is P(B|A) related to P(B)? to P(A)? (d) If B ⊆ A, how is P(B|A) related to P(B)? to P(A)?

Let A and B be events in sample space having positive probability. (a) If P(A|B) < P(A), show that P(B|A) < P(B). (b) If A ∩ B = ∅, what is P(B|A)? (c) If A ⊆ B, how is P(B|A) related to P(B)? to P(A)? (d) If B ⊆ A, how is P(B|A) related to P(B)? to P(A)?

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

5) Let A and B be events in sample space having positive probability.
(a) If P(A|B) < P(A), show that P(B|A) < P(B).
(b) If A ∩ B = ∅, what is P(B|A)?
(c) If A ⊆ B, how is P(B|A) related to P(B)? to P(A)?
(d) If B ⊆ A, how is P(B|A) related to P(B)? to P(A)?

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Expert Solution

Step 1: Define two events A and B

According to guide lines we are supposed to solve the first three subpart only rest can be resubmitted

Here A and B are two events in sample space with

P(A) >0 and

P(B) >0

Step by step

Solved in 4 steps with 4 images

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