Solution Found!
Let A,B,and C be events relating to the experiment of
Chapter 3, Problem 8TE(choose chapter or problem)
Problem 8TE
Let A,B,and C be events relating to the experiment of rolling a pair of dice.
(a) If
either prove that P(A)> P(B)or give a counterexample by defining events A, B,and Cfor which that relationship is not true.
(b) If
either prove that P(AB|C)> P(AB|CC) or give a counterexample by defining events A, B,and C for which that relationship is not true.
Questions & Answers
QUESTION:
Problem 8TE
Let A,B,and C be events relating to the experiment of rolling a pair of dice.
(a) If
either prove that P(A)> P(B)or give a counterexample by defining events A, B,and Cfor which that relationship is not true.
(b) If
either prove that P(AB|C)> P(AB|CC) or give a counterexample by defining events A, B,and C for which that relationship is not true.
ANSWER:
Step 1 of 2
Given that A,B and C are events relating in the experiment of rolling a pair of die
a) We have to prove that
Given that
Let us consider is conditioning on C and Cc
Then [By using the given inequalities]
Then
Hence we proved that