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Probability : Expected Values and Probability Distributions - According to an automobile manufacturer, the company uses 3,000 lock-and-key combinations on it's vehicles. Suppose that you find a key..

According to an automobile manufacturer, the company uses 3,000 lock-and-key combinations on it's vehicles. Suppose that you find a key for one of those cars. a) What is the expected number of vehicles that you would have to check to find one that fits your key? b) What is the probability that you would have to check

Modelling the Rules of a Game

Alex and Mark are playing a game. The goal is to get to 100. The first player picks a whole number from 1 to 10, inclusive, and then the second player picks a whole number from 1 to 10 and adds it to the score so far. The first player repeats this move. They continue this way. The player who makes the score exactly 100 wins.

Probability / Statistics : Combination Application Word Problems

In a marketing survey, consumers are asked to give their first three choices, of 9 different drinks. In how many different ways can they indicate their choices? Find the present value of an ordinary annuity with annual payments of $1,000, for 6 years, at 10% interest compounded annually. A class consists of 15 students.

Probability, Sets and Counting

All of the students at a college are majoring in psychology, business, or both. 73% of the students are psychology majors & 62% are business majors. If there are 200 students, how many of them are majoring in both psychology & business?

Probability and Expected Value.

The numbers 1 through 9 are written individually on nine cards. Choose three cards from the nine, letting x, y, and z denote the numbers of the cards arranged in increasing order. A. There are ____ ____ such as x, y, and z combinations. B. The probability of having x, y, and z all even is . C. The probability of ha

Random Variables : Probability Mass Function, Mean and Variance

A lot consisting of 100 fuses is inspected by the following procedure: 5 fuses are selected randomly, and if all 5 "blow" at the specified amperage, the lot is accepted. Suppose that the lot contains 10 defective fuses. Find the probabily of accepting the lot. HINT: Let X ba a r.v. equil to the number of defective fuses in

Probability-Conditional Prob. and Independence

The Question is: Suppose that each time that you buy a car, you choose between Ford and General Motors. Suppose that each time after the first, you stay with the same company with probability 2/3 and switch with probability 1/3. If you are equally likely to choose either company for your first car, what is the probability that


The Question is: In the game of bridge, each of 4 players is dealt 13 cards. If a certain player has no aces, find the probability that that person's partner has: a.)no aces b.)at least 2


In class we are learning about conditional probability and independence. The question is: On a multiple-choice test you know the answers to 70% of the question (and get them right), and for the remaining 30% you choose randomly among the 5 answers. What percent of the answers should you expect to get right?

Basic Probability

Please see attached file. --- Let A, B be mutually exclusive events and P(A) = 0.4, P(B) = 0.3 Find... ---

Probability - Frequency Of Dice Rolls

4. When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over. A. Why will some numbers come up more frequently than others? B. Each die has six sides numbered from 1 to 6. How many possible ways can

Probability and Independent Events : Bayes Theorem

5. (Sudden death) The NHL has another season-long strike, but the owners and players reach an agreement in June which leaves time for a highly abbreviated season. They decide that fans want to see the Stanley Cup decided, and so they play only a sudden-death version of the seventh game of the final round of the playoffs. Her

Find the probability of selecting each of the following...

Each individual letter of the word "pfeffernuesse" is placed on a piece of paper, and all 13 pieces of paper are placed in a hat. Three letters are selected at random from the hat. Find the probability of selecting each of the following. a) with replacement b) without replacement 1) Pulling T

Accounts Receivables Statistics - Tree Diagrams and Applications

An accountant found in a study that receivables fell into four categories: A: paid on time B: paid early C: paid late D: didn't pay Of a sample of 120 receivables she found that 35 were paid on time, 40 were paid early, 28 were paid late and the remainder were uncollectable. a) Using the results from the sample deter

Queueing Theory : Swimmers and Exponential Distribution

Queueing Theory Question 1 An average of 10 people per hour arrive (inter-arrival times are exponential) intending to swim laps at the local YMCA. Each intends to swim an average of 30 minutes. The YMCA has 3 lanes open for lap swimming. If one swimmer is in a lane, he or she swims up and down the right side of the lane.

Stochastic Processes : Poisson Process and Markov Chains

1. Suppose that shocks occur according to a Poisson process with rate A> 0. Also suppose that each shock independently causes the system to fail with probability 0 < p < 1. Let N denote the number of shocks that it takes for the system to fail and let T denote the time of the failure. (a) FindP{T>tNrrn}. (b) FindP{NrrnT=t}. (

Statistics : Standard Deviation and Mean (10 Problems)

1. True or False? The standard deviation of a population will always be smaller than the standard deviation of the sample means (of the samples used to estimate this same population). 2. The mean height for a population is 65 inches and the standard deviation is 3 inches. Let X_ denote the mean height for a sample of people

Statistics : Probability of Winning a Powerball Lottery

The Powerball For a single ticket, a player first selects five numbers from the numbers 1-53 and then chooses a powerball number, which can be any number between 1 and 42. A ticket costs $ 1. In the drawing, five white balls are drawn randomly from 53 white balls numbered 1-53, and one red Powerball is drawn randomly from


The sign "I LOVE MATHEMATICS" is put on the wall of the mathematics building at South Central Carolina Technical College. The letters start to fall off of the sign. Find the probability of each of the following events. 1.. The first letter that falls off is "M" . 2. The second letter that falls off is an "A" knowing tha

18 Problems : Payoff Tables and Decision Trees; Control Charts; Bayes Theorem; Total Quality Management ( Demings 14 Points of Management ), Expected Monetary Value, Red Bead Experiment

1. A tabular presentation that shows the outcome for each decision alternative under the various states of nature is called a: a. payback period matrix. b. decision matrix. c. decision tree. d. payoff table. 2. The difference between expected payoff under certainty and expected value of the best act without certainty is

Various Statistics Problems

1. Event A: You spend your entire Memorial Day 2006 in Acapulco. Event B: You spend your entire Memorial Day 2006 with some of your friends. TRUE OR FALSE: A and B are mutually exclusive events. 2.Event A: You spend your entire Memorial Day 2004 in Denver. Event B: You spend your entire Memorial Day 2004 in Vermont. TRU

Independent random variables

1. A coin is tossed 3 times. Discrete random variable X is equal to the number of times Heads comes up. Discrete random variable Y has the value 1 if the first toss comes up heads and 0 otherwise. (a) Find Pr[(X=1)n(y=1)] Are X and Y independent random variables?

Probability - drawing tokens

7. There are some tokens in a bag. Each token has a number ( a positive integer) printed on it. Ernesto does not know how many tokens are in the bag, and the only thing he knows about the numbers on them is that the mean of the numbers is 3 and the variance is 2. Ernesto is going to play a game in which he draws 1 token from th