(a) Prove that for events A and B, if P(B|A) > P(B) then P(A|B) > P(A).

Algebra and Trigonometry (MindTap Course List)
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Chapter14: Counting And Probability
Section14.FOM: Focus On Modeling: The Monte Carlo Method
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(a) Prove that for events A and B, if P(B|A) > P(B) then P(A|B) > P(A).
(b) A box contains four pieces of paper. Each paper has a note as follows: (1) "win prize
1", (2) "win prize 2", (3) "win prize 3" and (4) “win prizes 1, 2 and 3". One paper
is randomly selected. Let A; ={ "win prize i"} for i = 1, 2, 3.
i. Are events Aı, A2, A3 pairwise independent?
ii. Are events A1, A2, A3 mutually independent?
(c) A group of 20 people went out for dinner. Of those 10 people went to an Italian
restaurant, 6 to a Japanese restaurant and 4 to a French restaurant. We were told
that 8 people are satisfied with their meal in the Italian restaurant, 4 are satisfied with
their meal in the Japanese restaurant and 2 are satisfied with their meal in the French
restaurant. You meet someone the next day and he is satisfied with their meal:
i. what is the probability they went to an Italian restaurant?
ii. what is the probability they went to a Japanese restaurant?
ii. what is the probability they went to a French restaurant?
Transcribed Image Text:(a) Prove that for events A and B, if P(B|A) > P(B) then P(A|B) > P(A). (b) A box contains four pieces of paper. Each paper has a note as follows: (1) "win prize 1", (2) "win prize 2", (3) "win prize 3" and (4) “win prizes 1, 2 and 3". One paper is randomly selected. Let A; ={ "win prize i"} for i = 1, 2, 3. i. Are events Aı, A2, A3 pairwise independent? ii. Are events A1, A2, A3 mutually independent? (c) A group of 20 people went out for dinner. Of those 10 people went to an Italian restaurant, 6 to a Japanese restaurant and 4 to a French restaurant. We were told that 8 people are satisfied with their meal in the Italian restaurant, 4 are satisfied with their meal in the Japanese restaurant and 2 are satisfied with their meal in the French restaurant. You meet someone the next day and he is satisfied with their meal: i. what is the probability they went to an Italian restaurant? ii. what is the probability they went to a Japanese restaurant? ii. what is the probability they went to a French restaurant?
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