Problem 3Let A, B, and C' be three events in the sample space S. Suppose we know• AUBUC = S,• P(A) = },• P(B) = ,• P(AU B) = .Answer the following questions:a. Find P(An B).b. Do A, B, and C form a partition of S?c. Find P(C – (AU B)).

Answered: Image /qna-images/answer/929d0468-ced4-4d38-976e-3de7b3d6062c.jpg

Answered: Problem 3 Let A, B, and C' be three…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. Let A and B be two events such that ACB, then P(AB)= 1,2,3/Q1. (22 points)] This question consists of 11 paragraphs. In each part, circle the correct an a. P(A) d.0 b. P(A) c. P(B) 2. How many different four-digit numbers can be formed from the digits 1,2,3,4,5,6,7 such that the first digit 3 or 6 also you cannot repeat the digit. a. 240 b.48 c. 120 3. If A, B and C are mutually independent events and that P(A) = 0.3, P(B) = 0.2, P(C) = 0.4. The probability that at least one of the events occur is a. 0.336 c. 0.024 b.0.664 d. 0.976 e. None 4. A box contains 3 red balls and 5 black balls. Balls are drawn randomly one at a time with replacement from the box. The probability that the third red ball is the seventh ball drawn is. a. 0.169 b.0.282 c. 0.179 d. 0.121 e. None 5. A box contains 20 balls, 13 of them are red and the rest are blue. Three balls are drawn randomly without replacement. The probability of getting at least I blue ball is. a) 0.749 b) 0.251 c) 0.479 d) 0.521 a. 0.4 b.…
b)
4. A spinner is now created with four equal sized sectors as shown, An experiment is run where the spinner is spun twice and the outcome is recorded each time. (a) Create a sample space list of ordered pairs that represent the outcomes, such as (4, 2), which represent spinning a 4 on the first spin and a 2 on the second spin. 3 2 (b) Using your answer from (a), determine the probability of obtaining two numbers with a sum of 4.
1. Consider the following random experiment: there is a bag with 4 marbles in it, two red and two blue. We draw two marbles from the bag, without replacement. To make the sampling uniform, let's label the two red marbles R₁ and R2 and the two blue marbles B₁ and B2. Then the sample space is {R₁R2, R₁B₁, R₁B2, R2B1, R2B2, B1B2}. Finally, let X be the indicator variable equal to 1 if the two marbles drawn have the same color, and 0 if they have different colors. (a) Write down X as a function from the sample space to the real numbers. (b) What is Rx, the range of X? (c) Write down the probability mass function Px of X: this is a function from the range of X to the interval [0, 1]. (d) Identify the distribution of X by name, and give the parameter(s) of that distribution. (The functions in parts (a) and (c) of this problem both have only finitely many possible inputs. I don't care what notation you use in your answer, as long as you give me the value of the function for every possible…
For any two events A, B, and sample space S, state True or false: • If P(A) + P(B) = P(AU B) then P(AN B) = 0. • If P(AN B) = 0 then P(AU B) = P(A) + P(B). • The sample space, S, is always independent of any event A.
1. Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(AUB) =0ff Calculate P(A B).
2. The following table categorizes a group of people based on the flavor of Kool-Aid they drink andwhether or not they like Justin Bieber.grape cherry trop.punch Totalgrape cherry trop.punch Totaldoes like Bieber 30 15 88doesn’t like Bieber 58Total 52 176 The random experiment is to select one (1) person from the table out of the 176 people, at random.(a) Fill in the table.(b) What is the probability that the person doesn’t like Bieber?(c) What is the probability that the person likes cherry Kool-Aid?(d) What is the conditional probability that the person doesn’t like Bieber, given that the personlikes grape Kool-Aid?(e) What is the conditional probability that the person likes cherry Kool-Aid, given that the persondoes like Bieber?
. List the 10 possible samples (without replacement) of size 2 that can be obtained from the population of five officials. Lieutenant Governor (L) Secretary of State (S) Attorney General (A) Representative (R) Press Secretary (P) b. If a simple random sampling procedure is used to obtain a sample of two officials, what are the chances that it is the first sample on your list in part (a)? the secondsample? the tenth sample?
7. If an experiment the events A and B can both occur then a. P(A U B) = P(A)P(B|A) b. P(A N B) = P(A)P(A|B) c. P(AN B) = P(A)P(B|A) d. P(A U B) = P(B)P(B|A) %3D
1. Events A and B are mutually exclusive with P(A) = 0.280 and P(A or B) = 0.740 a) P(B)= b) P(Not A)= c) P(A and B)=
4. Suppose that a finite class contains 50% freshmen, 15% sophomores, 10% juniors, and the rest seniors. Suppose that 20% freshmen, 30% sophomores, 50% juniors, and 70% of seniors pass the class. Draw a tree diagram to represent this scenario: (a) Given that the student is a sophomore, what is the probability that she fails the class? (b) What is the probability that a randomly selected student passes the class? (c) What is the probability that a randomly selected student is a senior that passes the class?
3. Oil exploration : Let D and E be two events in a sample space. It is given that P (D) = 0.4, P (E) = 0.5 and P (DUE) = 0.8. (a) Are the events D and E disjoint? Are the events D and E independent? Then to oil exploration. We imagine two oil fields. The event B = "oil discovery on field 1", while the complementary event B' = "no oil on field 1". Similarly, the event C = "oil discovery on field 2", while C' = "no oil on field 2". We are given that P (B n C) = 0.06, P (B' n C) = 0.12, P (B n C') = 0.11 and P (B' n C') = 0.71. (b) Find the probability of oil on field 1. Assume that oil has been found on field 2. What is now the probability of oil on field 1? Assume that it has been proven that field 2 does not contain oil. What is now the probability of oil on field 1? Are events B and C independent?

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Problem 3 Let A, B, and C' be three events in the sample space S. Suppose we know • AUBUC = S, • P(A) = , • P(B) = , • P(AU B) = . Answer the following questions: a. Find P(An B). b. Do A, B, and C form a partition of S? c. Find P(C - (AUB).