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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


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 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 : 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

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

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


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


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 at random without any a

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 : Yahtzee and Die Tossing

1. Five fair dice are tossed once. Probability of Full House? Probability of Two Pairs? 2. A fair die is tossed n times. What is the probability that one face never appears?

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.


Two adults a1 and b1, and eight children c1, c2, ... , c8 board a bus with 10 seats s1, s2, ... , s10. The adults board first and randomly select seats. The children select seats in order with c1 selecting first, c2 selecting second, and so on. Each child sits in the lowest numbered seat available to them. What is the probab

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: 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

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 coin is flipped eight times where each flip comes up with either heads or tails how many possible outcomes? a) contain exactly 3 heads b) contain at least 3 heads c) contain the same number of heads n tails.

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


1. A lady has six cats. Each cat has a 0.60 probability of climbing into the chair in which the lady is sitting, independently of how many cats are already in the chair with the lady. Find the probability distribution for the number of cats in the chair with the lady. Find the expected number of cats in the chair with the lady.