1.5.2. There are 5 urns, numbered 1 to 5. Each urn contains 10 balls. Urn has defectiveballs, i = 1, ..., 5. Consider the following experiment: First an urn is selected uniformly (i.e. each urn isselected with the same probability) at random and then a ball is selected uniformly at random from theselected urn. The experimenter does not know which urn was selected.(i) What is the probability that a defective ball will be selected?(ii) If we have already selected the ball and noted that it is defective, what is the probability that itcame from urn 5? Generalise to urn &; & = 1,...,5.

Answered: Image /qna-images/answer/9868a7d1-dfc1-434f-b02b-57bb9e8983cc.jpg

Answered: 1.5.2. There are 5 urns, numbered 1 to…

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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An urn contains two red balls and five blue balls A. Draw three balls at random drom the urn, without replacement. Compute the expected number of red balls in your sample. B. Draw three red balls at random from the urn, with replacement Compute the expected number of red balls in your sample.
17. 25 athletes are participating in jumping competition. They are of different nationality: 8 from Argentina 6 from Brasil 5 from Paraguay 6 from Uruguay To determine an order in which athletes participate, lot is drawn. Find out the probability that last athlete to participate is from Argentina.
Q4i) Hospitals records indicated that cardiac patients stayed in the intensive care unit of the hospital for the following number of days. Number of days stayed Frequency 4 32 5 18 6 25 7 19 3 10 Find the probabilities : a) A patient stayed exactly 7 days b) A patient stayed almost 6 days c) A patient stayed at least 5 days Q4.ii) a) Write the sample space if three (3) coins are tossed at a time. b) Find the probability of having at least 1 tail.
1.Suppose a fair coin and a fair die is tossed and A is an event that an even number and a tails appear, what is the number of outcomes in A? 2.Let X be a random variable that denotes the number of heads which appear in tossing a coin twice. Which of the following cannot be a value of the random variable X?
1. An experiment consists of flipping a coin until either heads is flipped 6 times, or the same side shows up 3 times in a row. The random variable X assigns the number of total coins flips to each outcome. What number is assigned to HTTT? 2. A person picks a number between 1 and 28536. The random variable Z assigns the number picked to each outcome. What number is assigned to 267927? 3. A person picks a number between 1 and 285336. The random variable Z assigns the 0 to an even number 1 to an odd number. What number is assigned to 267927?
Q1) A specific article is produced by machines M, M, M,and M. The probability that a random article is produced by M, Mə and Ma is 0.2,0.3 and 0.1 respectively. The probability for each machine to produce defective articles is given as M, = 0.03, M2 = 0.02, M, = 0.04 and Ma 0.01. What is the probability that a random article was made by Ma, given that it is non-defective?
4. Suppose that a committee of 2 is selected at random from a group of students that consists of 6 seniors and 4 freshmen. Find the expected number of freshmen in the committee. 0.8 0.9 O 1.6 O 14 5. Let A and B be two events in a sample space S with P (A) = 0.6, P (B) = 0.3 and P (A U B) = 0.7 Find P (AB)
1. A fair coin is tossed 20 times. Find the probability of obtaininga. less than 8 heads b. more than 6 headsc. between 6 and 10 heads inclusive 2. A coin is weighted so that the probability of obtaining a head in a single toss is 0.4. If the coin is tossed 25 times, determine the probability of obtaininga. less than 10 headsb. between 10 and 12 heads inclusivec. more than 15 heads 3. A basketball player has a 75 percent chance of making a free throw. What is the probability of his making 100 or more free throws in 120 trials? 4. A marksman’s chance of hitting a target with each of his shots is 60 percent. If he fires 30 shots, what is the probability of his hitting the targeta. at least 20 times? b. less than 10 times?c. between 15 and 20 times inclusive? 5. A marksman’s chance of hitting a target with each of his shots is 60 percent. If he fires 30 shots, what is the probability of his hitting the targeta. at least 20 times? b. less than 10 times?b.…
. Assume that the box contains balls numbered from 1 through 28, and that 3 are selected. A random variable X is defined as 3 times the number of odd balls selected, plus 4 times the number of even. How many different values are possible for the random variable X?

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