If A and B are events which are conditionallyindependent given a third event C, which of thefollowing is not necessarily true?Select one:O a.P(An B|Cº) = 1 – P(A|C)P(B|C)O b.P(BANC) = P(B|C)O c. None of the other choicesd. P(An B|C) = P(A|C) – P(A|C)P(Bª|C)O e. P(An BnC) = P(A|C)P(BC)

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Answered: If A and B are events which are…

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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A cell phone salesperson has kept records on the customers who visited his store. Forty percent of the customers who visited the store were female. Furthermore, the data show that 35% of the females who visited his store purchased a cell phone, while 20% of the males who visited his store purchased a cell phone. Let A1 represent the event that a customer is a female, A2 represent the event that a customer is a male, and B represent the event that a customer will purchase a phone.What is the probability that a female customer will purchase a cell phone?
Suppose that events A and B are independent; A and C are independent ; B and C are also independent. If P(A) = 0.3, P(B) = 0.4, P(C) = 0.5, what is P(A ∩ B ∩ Cc )? a). 0.3 b). 0.4 c). 0.6 d). 0 e). none of above
16. Given that two events A and B are mutually exclusive, P(An B) is: a. b. C. d. 17. At a pet store you can choose between 6 fish species, 2 mini frog species, and 4 plant species. You want your tank to contain one fish, one frog, and one plant. How many different setups are possible for your tank? a. 12 b. 48 C. 3 d. 0 0.50 1 None of these a. b. 18. A set of data is normally distributed with a mean of 7 and a standard deviation of 2.5. Calculate the z- score for the data value x = 5: C. d. 122 0.80 -0.80 0.90 -0.90
Determine if events A and B are independent. 7 P(A and B) 20 7 13 P(B) : 20 13 P(A and B) 20 169 4) = P(B) = 2) P(A) = 100 400 7 3) Р(A) %—D 10 P(B) = 5 21 1 P(B) 1 P(A and B) 5 1 P(A and B) 4) Р(A) — 100 25
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
. Given events A, B and C such that A and B are mutually exclusive, A is a subset of C, P(B) = 1/2, P(C) = 3/4, P(B and C) = 3/8, and P(A and C) = 1/4, Calculate: P(A) P(C and notA) P(B or C) P(notA or B) P(B | notC)
You are given the following information on Events A, B, C, and D. Compute P(D). A. Compute P(A ∩ B). A. Compute P(A | C). A.
5. Show that the conditional independence of A and B given C neither implies, nor is implied by, the independence of A and B. For which events C is it the case that, for all A and B, the events A and B are independent if and only if they are conditionally independent given C?
4. 60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation – e.g., P(A|B) =..) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?

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