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# Probability

### 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 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&#9474;A) = 0.3, then P(A and

### 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

### Statistics/Probability

Sample frequency of success. See attached file for full problem description.

### 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

### Probability Mass Functions and Independent Events

Let F(x)=.... (a) Show that F(x) is a distributiion function of a discrete random variable. (b) Find the corresponding PMF. Let X have a distribition function F(x) = (1 - 2^-x)I[0,oo)(x). Define the following events: A = {X > 1) B = {X >2) U {X <log2(4/3)} C = {X > 3) U {X <log2(S/7)} U {log2 8/5 <X <log2(8/3)} D = {X > 5

### Probability (Random Variables)

Distribution, Density Functions. See attached file for full problem description.

### Probability : Independent Events and Hemophilia

1.(a) Let. A, B, C are mutually independent. Prove that A. is conditionally independent of B given C. (b) Assume that A, B are both independent and conditionally independent given C. Is it necessary that A, B, C are mutually independent? 2. Hemophilia is a hereditary disease. If a mother has it, then with probability 1/2, an

### Probability : Sampling without Replacement and 'Three Doors' Problem

1. Urn I and Urn II each contains 3 red and 3 white balls. First we transfer one ball from Urn I to Urn II. Then we transfer one ball from Urn II to Urn I. Finally we sample one ball from Urn and it is red. What is the probability the both transferred balls were also red? 2. In the famous "Monty Hall game" there are 3 doors.

### To find joint probability table and to test if the hotel has good customer service.

1. Chapter 1 - Problem 18 The General Store at State University is an auxiliary bookstore located near the dormitories that sells supplies, toiletries, sweatshirts and t-shirts, magazines, packaged food items, and canned soft drinks and fruit drinks. The manager of the store has noticed that several pizza delivery service

### Probability of Given Patient with a Serious Illness

Researchers have determined that patients who are smokers have 18% chance of contracting a serious illness, whereas only .06 probability that a non smoker will contract a serious illness. 23% are all smokers 77% non smokers What is the probability that a given patient if the patient has a serious illness?

### Solve linear equations and compounding interest

An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse. The National Tree Lighting Ceremony is held annually on the Ellipse. Because the President officiates at this event, the Secret Service makes calculations which they use

### Solve linear equations and compounding interest

Among the professionals you have interviewed for your article, were several state and federal government spokespersons who use linear equations in a variety of ways. An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse.

### Real-Life Applications of Parabolas, Hyperbolas and Probability

One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the bridge span; the force of the typical water currents wearing

### Probability

Probability: Mary is taking two courses, photography and economics. Student records indicate that the probability of passing photography is 0.75, that of failing economics is 0.65, and that of passing at least on of the two courses is 0.85. Find the probability of the following: a.Mary will pass economics. b. Mary will pass both

### Expected Value Probability Problem

Please open the attached excel and word files for the example. Assume I am valuing the cash flows of a simple company with contracts 'a' through 'f' that have different varying cash flows over 10 years. Probability of default for each contract a-f in any given year = 2.50%. Once there is a default, the cash flows cease a

### Forecasting model for soft drinks

The number of cans of soft drinks sold in a machine each week is recorded below from left to right, with oldest data to the left of the table.... see attached