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Probability

Probability and Birthdays

From a set of n randomly chosen people, let Eij be the event that persons i and j have the same birthday. Assume that each person is equally likely to have any of the 365 days of the year as his or her birthday. Find a) P(E3,4|E1,2) b) P(E1,3|E1,2) c) P(E2,3|E1,2∩E1,3) See attached file for full problem description.

Probability, Random Variables and Density Functions

1. A coin is biased so that a head is three times as likely to occur as a tail. Find the expected number of tails when this coin is tossed twice. 2. An attendant at a car wash is paid according to the number of cars that pass through. Suppose the probabilities are 1/12, 1/12, ¼, ¼, 1/6, and 1/6, respectively, that the a

Quantitative Methods : Random Numbers and Probability Distributions

I/ Explain why a decision maker might feel uncomfortable with the expected value approach, and decide to use a non-probabilistic approach even when probabilities are available. II/ 1. ________________ is a technique for selecting numbers randomly from a probability distribution. 2. Random numbers of a mathematical proc

Mutually exclusive events: Example problem

Can a mutually exclusive events be independent at the same time? I know that Binomial distribution is not another representation of a discrete probability distribution, but an example. Can you give two other ways of representing a discrete probability distribution? Or Can a pair of events be both mutually exclusive and indepe

Probability

Please show answers with all steps. 1. A binary message is sent over a noisy channel. The message is a sequence x1, x2, . . . , xn of n bits (xi 2 {0, 1}). Since the channel is noisy, there is a chance that any bit might be corrupted, resulting in an error (a 0 becomes a 1 or vice versa). Assume that the error events are

Probability

Problem 3: Suppose that a batch of 100 items contains 6 that are defective and 94 that are nondefective. If X is the number of defective items in a randomly drawn sample of 10 items from the batch, find a) P(X = 0) b) P(X > 2)

Probability and Statistics

(a) Explain the difference between mutually exclusive and independent events. Can a pair of events be both mutually exclusive and independent? Give examples. (b) Discuss the problems inherent in using words such as "likely," "possibly," or "probably" to convey degree of belief. (c) One way a discrete probability distribu

Probability and Combinations

1. Assume you have five cards are chosen from a standard deck of 52 playings cards. How many hands contain four aces? 2.You have 15 computer monitors, of which three are defective. If you randomly chooses five monitors, how many different sets can be formed that consist of three non-defective and two defective monitors?

Quantitative Methods

1. Administrators at a university will charge students $200 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $35 per student for the administrators to provide the course materials. How many students (whole numbers) would have to register for the seminar for th

Quantitative Methods : Probability and Break-Even Points

1. Administrators at a university will charge students $200 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $35 per student for the administrators to provide the course materials. How many students (whole numbers) would have to register for the seminar for th

Joint and Marginal Probability Tables

I own three fuel terminals. one in the north, one in the south and one in the mid-west. My north terminal house 25% of my employees, my south terminal house 40% of my employees and my mid-west house 35% of my employees. 10% of my north employees failed a management test, 15% of my south and 5% of my mid-west. Using excel I'm

Conditional Probability Example

I'm trying to set up an excel spreadsheet to solve a statistical probability. Patients 23% (smokers) -18% have a chance of contracting a serious illness 77% (non smoker) - 6% have a chance of contracting a serious illness I'm trying to figure out the probability that a given patient is a smoker if the patient has a ser

Probability of Consecutive Birthdays

Please help solve the following problem. Please provide step by step calculations with explanations. Given 20 people, what is the probability that among the 12 months of the year there are 3 non necessarily consecutive months containing exactly 4 birthdays? hints: 1. to count the number of elements of the state space,

Probability & Statistics

1. Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 east between meals, 122 smoke and drink alcoholic beverages, 83 east between meals and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these bad health practices. If

Probability & Statistics

Here are a set of problems that I would like to learn how to do the steps to. I have also prepared the questions with the answers, however would like to see the process in which the answers were derived. (See attached file for full problem description) --- 1. If P(A) = 0.5, P(B)= 0.4, and P(B│A) = 0.3, then P(A and

Probability

An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) the same color (b) different colors

The following cost table is associated with a decision...

(See attached file for full problem description) --- The following cost table is associated with a decision: States of Nature Decision Options S1 S2 S3 A 200 100 50 B 125 110 80 C 100 130 90 The probabilities of the states of nature are P1 = 0.55, P2 = 0.25, P3 = 0.20 a. Lay out the decision tr

Frequency Distributions, Histograms and Probability Analysis

Find the roots of x2 + 3x - 39 using Goal Seek For the following frequency distribution: a. Plot the frequency distribution b. Calculate E(x) c. Calculate P(x2) d. Calculate P(x<=400) x freq 150 3 300 8 400 6 450 4 650 2 900 1 1020 1 Problem 5

Probability Described Symbols

USE WORDS TO DESCRIBE THE SOLUTION, not just symbols 20 workers are to be assigned to 20 different jobs. How many different assignments are possible?

Probability Theory: Proving a Limit

Show: lim(as r-->0)[r + x - 1]*[(p^r)(1 - p)^x]/(1-p)^r=[(1-p)^x][-x(log(p))] x for x = 1,2, ... Please view the attached file for proper formatting of this question.

Probability

Attached is a copy of an Excel spread sheet, ?This spreadsheet contains 4 worksheets oWorksheet #1: Lists the random numbers you use for your simulation. There are three sets, with each set having up to 50 numbers. Use each set for each type of randomization. For example, on problem 9, you will use the first set to rando

Probability : Events

Let A and B be events, both having positive probability. Show that if P(A|B) > P(A), then P(B|A) > P(B). We know the following definitions: Conditional Probability: The probability of event B given event A is P(B|A)=P(AandB)/P(A) The probability of event A given event B is P(A|B)=P(Aand B)/P(B) Independent Events: T

Solve the Probability Word Problem

See the attached file. Jan's big brown dog Shtutzy has recently learned how to open the fridge. One day Jan leaves a dozen (12) eggs in the fridge. Two of the eggs are rotten. the rest are good. When Jan comes home, the fridge is ransacked. Among other things, Shtutzy ate 5 eggs out of the dozen. Assume that she picked the eggs