An urn contains 10 balls, of which u are black and 10 – u are white. Balls aredrawn at random, one at a time, their colour recorded and then put back. Thishappens N times.What is the probability that the black ball is drawn ng times?What is the expectation of ng? What is its variance? Evaluate these at theexample values of N = 5 and N = 400, with u = 2 in each case.

The urn contains u black and 10-u white balls, total 10 balls. N balls are drawn from the urn and…

Answered: An urn contains 10 balls, of which u…

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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There are 4 red balls, 6 blue balls and 2 white balls in a bag. Suppose on every single turn, yourandomly select a ball, see the color of it and put it back in the bag. You keep doing thisrepeatedly.a. What is the probability that you get the first red ball on the 5th turn?b. How many turns are expected to get one non-white ball?c. What is the variance of the number of turns required to get one blue ball?
A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Y1 = 0, if the policy holder does not have any health issues; Y1 = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).
Based on a survey, assume that 33% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when six consumers are randomly selected, exactly three of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting three consumers comfortable with drones followed by three consumers not comfortable, as in this calculation: (0.33)(0.33)(0.33)(0.67)(0.67)(0.67) = 0.0108? Choose the correct answer below. A. The event that a consumer is comfortable with drones is not mutually exclusive with the event that a consumer is not comfortable with drones. B. The probability of the second consumer being comfortable with drones cannot be treated as being independent of the probability of the first consumer being comfortable with drones. O C. There are other arrangements consisting of three consumers who are comfortable and three who are not. The probabilities corresponding to those other…
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After careful research you observe that the number of hackers active on each day is a random variable Bin(3,0.5) distribution. If no hackers are active, the probability of the website failure is 0.15; If one hacker is active the probability of the website failure is 0.3; if two or more hackers are active the probability of the website failure is 0.5. You conclude that the total probability of website failure on a given day is two decimal place). Assuming there is a failure, the probability no hackers are active is (to (to two decimal places).
All human blood can be "ABO-typed" as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in a country. Blood type A National probability 0.43 0.12 AB ? (a) What is the national probability of type AB blood? O 0.41 (b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen person from this country can donate blood to Maria?
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4. A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Yı = 0, if the policy holder does not have any health issues; Yı = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).
2. A department store receives an average of 5 returned items per day. The probability that a returned item has an available replacement is 0.65. [Hint: there are two separate distributions here.] d. e. f. Calculate the probability that there are 4 returned items and none has available replacements in a certain day. Calculate the variance and the mean of the returned items. Calculate the variance and the mean of the replaced items. 2
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