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Three questions about probability

(1) An instructor obsessed with the metric system insists that all multiple-choice questions have 10 different possible answers and only one is correct. What is the probability of answering correctly if a random answer is picked? An event is unusual if probability is 0.05 or less, so is it unusual to answer the question by c

Seven households and other questions

Seven households have the following number of creatures living there, 6,5,8,9,7,8,9. The standard deviation of creatures living in these households? Give the five number summary of distribution for creatures living in these houses. --- 30% of people own a house with one garage, 40% own a house and parking space,

Simulation of random numbers using STATDISK

Probabilities through Simulations 1)Dice Simulation - Use Statdisk to simulate 1000 rolls of a pair of dice. Sort the results, then find the number of times that the total was exactly 7. ___________. Based on that result, estimate the probability of getting a 7 when two dice are rolled._____________. How does this es


66. Ninety students will graduate from Lima Shawnee High School this spring. Of the 90 students, 50 are planning to attend college. Two students are to be picked at random to carry flags at the graduation. a. What is the probability both of the selected students plan to attend college? 1. P (A) + P (B) = b. What is the

Jerry can open up a small shop, large shop, or no shop

Jerry can open up a small shop, large shop, or no shop. There will be a 5 year lease on a building he wants to make the correct decision. Jerry is also thinking about hiring a consultant to conduct a market research study. If the study is conducted, the results could be either favorable or unfavorable. Develop a decsion tree

Probability questions: Gaussian approximation and Poisson approximation

Probability: 1.You flip a coin n times.Please answer the following questions about the fraction f of the tosses that show heads. A. Lets say n=100. Compute exactly the prob that the fraction of the coins showing heads is f=0.5 B. Say n=100 and consider the prob that f=0.5. Show that this probability can be approximated us

Statistics question

Suppose that during a football game, lemonade sells for $15 per gallon but only costs $4 per gallon to make. If they run out of lemonade during the game, it will be impossible to get more. On the other hand, leftover lemonade has a negligible value. Assume that you believe the fans would buy 10 gallons with probability 3/10, 11

Decision Tree and Statistics

I need some help with this question containing a decision tree and analysis: Bob is a second year MBA student contemplating his employment situation. He has three prospects: • He has a "standing" offer from Company A for $65K. This offer does not expire. • He has an "exploding" offer from Company B for $75K. This offe

Calculations for Probability

1. For each of the following stats, prove the below or give counterexamples: a. If 2 events A & B are independent, then A & B' are also independent. b. Let's say that 3 events A,B,C have probabilities satisfying P(ABC)=P(A)P(B)P(C),then the events A & B are independent. c. If P(A|B)>P(A), then P( A|B' )< P(A). (you may assume

Probability Theory

Find the distribution function. See attached file for full problem description.

Probability Theory

(See attached file for full problem description) Two fair dice have both had two of their sides painted red, two painted black, one painted yellow and one painted white. (a) when this pair of dice is rolled, what is the probability that both will show the same color? (b) What is the probability that only one of the dice wil

Problems on Basic Probability

8. A sample of 2,000 licensed drivers revealed the following number of speeding violations. Number of Violations Number of Drivers 0 1,910 1 46 2 18 3 12 4 9 5 or more 5 Total 2,000 1. What is the experiment? 2. List one possible event. 3. What is the probability that a particular driver had

Random Probability and Statistics

1. Each vehicle in Mexico is either a truck, car or bicycle. Also each vehicle is red, green or yellow. We pick a vehicle at random. The following are known facts: 1. There's a 30% chance that vehicle is truck 2. There's 50% chance that vehicle is red 3. There's 20% chance that vehicle is a red truck 4. The vehicle is

Critical Flight Paths

Two airlines offer conveniently scheduled flights to the airport nearest your corporate headquarters. Historically, flights have been scheduled as reflected in this transition matrix. Current Flight Next Flight Airline A Airline B Airline A .6 .4 Airline B .2 .8 If your last flight was on B, what is the probabili

Solving Various Probability Problems

(See attached file for full problem description) --- 1. A food distributor carries 64 varieties of salad dressing. Appleton Markets stocks 48 of these flavors. Beacon Stores carries 32 of them. The probability that a flavor will be carried by Appleton or Beacon is 15/16. Find the probability a flavor is carried by both A

Sample Probabilities

In a city, 60% of the voters are in favor of building a new park. An interviewer intends to conduct a survey. a. If the interviewer selects 20 people randomly, what is the probability that more than 15 of them will favor building the park? b. Instead of choosing 20 people as in part a, suppose that the interviewer wants t

Exponential Distribution to Determine Product Lifetimes for two Products

A consumer is contemplating the purchase of a new compact disc player. A consumer magazine reports data on the major brands. Brand A has lifetime (TA) which is exponentially distributed with m=.02; and Brand B has lifetime (TB) which is exponentially distributed with m=.01. (The unit of time is one year). a. Find the expec

Probability Generating Function

Let X1, X2,... be i.i.d. random variables with p.g.f Gx(s) and N be a r.v independent of X with p.g.f. Gn(s). Define S=X1+X2+...+XN. Find Var(S) in terms of expectations and variances of X and N.

Integrate an Inequality and Find a Density Function

1. Prove that for all x > 0 (1/x - 1/x^1)phi(x) < 1 - ohi(x) < (1/x)phi(x) Hint: Integrate the following inequalities: (1 - 3y^-4)e^(y^2/2) < e^-(y^2)/2 < (1 + y^-2)e^-(y^2)/2. 2. Let X be a random number from (0,1) (ie. X ~ uniform (0,1)). Find the density function of (a) Y _ -log(1-X), (b) Z _ X^n. See attachment f

Blonde hair probability problem

In a sample of 2400 people, 170 have blonde hair. Two unrelated people are selected at random... (See attached file for full problem description)

Quality Management

(See attached file for full problem description) --- 1. A study determines that 60% of the voters in a town intend to vote for the incumbent mayor. If a sample of 8 people is selected, the approximate probability that 6 of the 8 people surveyed intend to vote for the incumbent is (using the binomial probability formula): a.


A card is picked up at random from a standard deck of 52 cards.Find the odds that the card is a heart.

Binomial Probability

Consider a gambler who at each play of the game has probability of winning one unit and probability of loosing one unit. Assuming that the successive plays of the game are independent, what is the probability that, starting with units, the gambler's fortune will reach

Simple Probability Problems

1. Suppose you have 3 nickels, 2 dimes, and 6 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that a. You will draw a dime? b. You will draw a half-dollar? c. You will draw a quarter? 2. You are rolling a pair of dice, one red and one green. What is the probability

Probability questions

A) A shipping form keeps 2 cars in readiness for local delivery. Because of demands on their time and the frequency of mechanical failure, the probability that a particular car will be available when needed is 0.9. The availability of one car is independent of the availability if other. a) If both cars are wanted at the sam

Probability questions

Records of a department store show that 5% of customers who make a purchase return the merchandise for refund. Of the remaining customers, 9% return the mechanise in order to exchange it. a) In the next six purchase, what is the probability that at most one will return for refund? b) In a sample of eight customers, exactly

Subjective Probability of a Capital Investment Firm

Suppose that an executive of a venture capital investment firm is trying to decide how to allocate his funds among three different projects, each of which requires a $100,000 investment. The projects are such that one of the three will definitely succeed, but it is not possible for more than one to succeed. Looking at each p

Probability problem marginal analysis

Working on below problem to identify error as presented. "On the fictitious game show "Marginal Analysis for Everyone" the host subjects contestants to unusual tests of mental skill. On one, a contestant may choose one of two identical envelopes labeled A and B, each of which contains an unknown amount of money. The host