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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14. Event A and Event B are dependent. 21 a) P(B)=; p(A and B) 200 P(B|A) = b) P(B|A) = ; P(A and B) P(B) = 200
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
Step 4: Now calculate the probabilities P(AC) and P((A ∩ B)C) by first listing the simple events in AC and (A ∩ B)C. There are five simple events E1, E2, ..., E5. The complement of A is the collection of simple events that are not in A. We are given that A = {E2, E3}, so AC consists of the following event(s). (Select all that apply.) E1 E2 E3 E4 E5 We previously found that A ∩ B = {E2}. Therefore, the complement (A ∩ B)C includes the following event(s). (Select all that apply.) E1 E2 E3 E4 E5
Events whose probability of their intersection is the product of their individual probabilities and is more than 0 are called? Select one: a. complement b. mutually exclusive. c. conditional d. independent
The following sample observations on total coating layer thickness (in μm) of10 wire electrodes, as shown in Table 3. (a) Calculate a 99% two-sided CI for the standard deviation of the coating layer thickness distribution. (b) Is this interval valid whatever the nature of the distribution? Explain.
In this version of the Monty Hall problem, there are 4 doors with a car behind one of them and goats behind the other 3. You pick a door. Monty then shows you two doors that have goats behind them. He then asks you if you want to stay with your original pick or switch to the unopened door. Let A be the event that you win the car. Let B be the event that you stay with your original pick. What is p(A | B)? 1/4 1/3 1/2 2/3 3/4
a) Show that for any three events A, B, and C, the probability that at least one of them occurs is P(A) + P(B) + P(C) - P(An B)- P(ANC) - P(BNC) + P(An BnC). b) Given A and B are independent events, with P(A) = 0.50 and P(B) = 0.30. Find P(ANB) c) About 52% of the residents of Capricorn municipality are happy and 48% of the residents are not happy with the delivery service. A recent study showed that 75% of happy residents and 25% of the unhappy residents are in favour of keeping the mayor of the municipality. If resident is randomly selected from the municipality residents is found to favour the motion. What is the probability that this person is happy with the delivery service?
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?
3. All of the morning math classes are filled & Lisa has a decision to take either Mrs. Fowler or Mr. Williams in the afternoon, what is the probability of Lisa taking a Mrs. Fowler or Mr. Williams in the afternoon? 4. Lisa's school counselor informs her all of Mrs. Fowlers classes are filled. The school adds another teacher Mrs. Jackson. She will teach (1ª, 3rd, 5th, and 6th). What is now the probability of getting Mrs. Jackson for math in the morning?

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