Problem#3: Consider an experiment in which each of three cars taking aparticular freeway exit turns left or right atroad. Create the sample space for all the possible outcomes of thisthe end of a certainexperimentProblem#4: From the previous experiment in which each of three carstaking a particular freeway exit turns left or right at the end of acertain road. Write the event that exactly one of the three cars turnsright, the event that at mostone of the cars turns right and theevent that all three cars turn in the same direction.

We know, Sample Space is set of all possible outcomes of the experiment. It is denoted by S. and…

Answered: Problem#3: Consider an experiment in…

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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P3. Four identical urns each contain three balls. In urn I, all 3 balls are black, in urn II, 2 black and 1 is white, in urn III, 1 is black and 2 are white, and in urn IV, all 3 are white. One of the urns is picked at random, and a ball is chosen from that urn, which turns out to be white. (a) What is the probability that all 3 balls in the selected urn are white? (b) A second ball is picked from the selected urn and is also found to be white. Now, what is the probability that all 3 balls in the selected are white?
Problem 2 An urn contains 5 white balls and 7 black balls. Draw a ball and do not put it back into the urn. Then draw a second ball. (1) Define an appropriate probability space (2,A,P) to describe the experiment. (2) Describe the following events as subsets of the sample space : W₁ = "The first ball is white" B₁: "The first ball is black" W₂: "The second ball is white" B₂: "The second ball is black" (3) Compute P(W₂ | W1₁), P(W₂ | B₁), and P(W₂). (4) Are W₁ and W₂ independent? Justify your claim mathematically!
Question d and e for the first probem. Question b, c and d for the second problem.
Please do #4
the accident. Question 16 Shashank performs an experiment comprising a series of independent trials. On each trial, he simultaneously flips a set of Z fair coins. a. Given that Shashank has just had a trial with Z tails, what is the probability that next two trials will also have this result? b. Whenever all the Z coins land on the same side in any given trial, Shashank calls the trial a success. i. Find the PMF for K, the number of trials up to, but not including the second success. Find the expectation and variance of M, the number of tails that occur before the first success where Z = 3 in this case. ii. (Hint: Write M = X, + X2 + .…+ Xy Where X; is number of tails in that occur on unsuccessful trail i and N is number of unsuccessful trails and find E (M) in terms of E (X) and E(N) and for var(M) first write in terms of M | N (i.e. M given N) and later write var(M) in terms of E(N), E (X), var(N), var(X) using the above derived variance equation in terms of M | N.) You are expected…
Question 2. Two companies A and B are offering 70 and 50 products respectively. Company A is offering 40 software products and 30 hardware products. Company B is offering x hardware products and y software products to be determined. If a product is selected at random, what is the probability that (a)This product is a hardware product given that is from company B? (in terms of y) (b)This product is a hardware product given that is from company A? (C) For what values of y will the probability in part (a) be greater than the probability in part (b)?
Problem 2 We regard the Norwegian population of people over 60 years old: i. 80% will be fully vaccinated against Covid19 before the end of May. ii. 20% own a holiday flat abroad. iii. 16% will be fully vaccinated against Covid19 before the end of May and owWn a holiday flat abroad. A Norwegian person over 60 years old is drawn at random. We define two events: A: The person will be fully vaccinated against Covid19 before the end of May. B: The person owns a holiday flat abroad. a) Calculate P(AUB) b) Calculate P(A®OB°)and give an interpretation of your result. c) Calculate P(A|B) and give an interpretation of your result. d) Are A and B independent events? Explain your answer.
Problem 8 There are 40 students in STA201 section Z. Mr. Tausif picked 10 students' names and kept his selection secret. Mr. Shehran and Ms. Lubaba chose 5 and 6 students' names respectively without telling each other about their selections. (There might be common students within Mr. Shehran's list and Ms. Lubaba's list). What is the probability that exactly 2 of Mr. Shehran's chosen students and 3 of Ms. Lubaba's chosen students match the 10-student list of Mr. Tausif r Problem 9 A microprocessor production plant produces chips of three categories: Grade A, Grade B, and Grade C. Every single chip goes through rigorous testing before being sent out to the stores. For every 50 Grade A chips that are tested, 32 pass, 12 fail, and the remaining chips are sent to be re-tested. For every 75 Grade B chips, 45 pass, 24 fail, and the rest are re-tested. And for every 60 Grade C chips, 23 pass, 17 fail, and the rest are re-tested. The plant distributes its production of Grade A, B, and C chips…

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