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Probability

Probability: Random Selection

Two balls are drawn in succession from a box containing 4 red and 2 white balls. a) What is the probability of drawing a red ball on the second draw if the first one is not put back in the box after it is drawn? b)What is the probability of drawing a red ball on the second draw if the first one is put back in the box after it

Probability

In order to test a new car, an automobile manufacturer wants to select 4 employees to test drive the car for one year. If 12 management and 8 union employees volunteer to be test drivers and the selection is made at random, what is the probability that at least one union employee is selected?

Probability Question : Expected Value

Tom and Jim decided to play the following game for points. A single die is rolled. If it shows a non-prime number, Tom receives points equal to two times the number of dots showing. If it shows a prime number, Tom loses points equal to three times the number of dots showing. What is the expected value of the game?

Probability

Each of the numbers 1 through 10 inclusive has been written on a separate piece of paper. The 10 pieces of paper have been placed in a hat. If one piece of paper is selected at random, with replacement, find the probability that the number selected is: a. greater than 3 b. even c. odd or greater than 3 d. odd or less than

Probability

In her wallet, Susan has 12 bills. 6 are $1 bills, 2 are $5 bills, 3 are $10 bills, and 1 is a $20 bill. She passes a volunteer seeking donations for the American Red Cross and decides to select 1 bill at random. Determine: a. probability she selects $ 5 bill (my ans: 1/5) b. probability she does not select a $5 bill (my ans

Probability : Counting Principle

A social security number has 9 digits. How many different S.S numbers are possible if: a. repetition of digits is permitted b. repetition of digits is not permitted c. the first digit cannot be a 0 and repetition is not permitted I need the layout (counting principle) ex. 9 8 7 - 6 5 - 2 1 4 3 - - - - - - - -

Probability : Combinations

Mr james just won 6 tickets for each of 2 consecutive Giants home football games. For the first game, Mrs James will not be able to attend so he has 5 extra tickets. He will invite 5 of his 9 closest friends from work to go with him. Mr. and Mrs. James will both attend the second game. They have 4 extra tickets and are consideri

Probability: Joint Probability Mass Function, Covariance and Variance

Let X and Y have joint probability mass function Pr{X = i, Y = j}= c(i + 1)(j + 2) for i >= 0, j >= 0, and i + j < 4. Determine a) the marginal probability mass function of X b) the probability mass function of Y c) the conditional probability mass function of X given Y = 0 d) the probability mass function of Z = X + Y

Probability: Variance, Mean and Standard Deviation

1) Suppose we have an aisle with storage racks on both sides of the aisle. The aisle is 100 feet long. A worker is stationed at one end of the aisle. The worker needs to retrieve an item from storage. Assume that the items are divided into two groups: high turnover and low turnover. The high turnover items are stored in the loc

Random Variables : Continuous R.V., Exponenetial, R.V, Mean and Variance

3) Let X be a continuous random variable with probability density function f(s)= c(1 + s^2) for -2 <= s <= 2. a) Determine c b) Determine Pr {X <= 0} c) Determine the mean of X d) Why is the previous answer fairly obvious? e) Determine the variance of X f) Compute Pr {X = 2 | X = 0} g) Determine the cumulative distribut

Probability: Moment Generating Functions and Poisson Process

1.) Let X be a discrete random variable with probability mass function Pr {X=k} = c(1+ k^2) for k= -2, -1, 0, 1, 2. a) Determine c. b) Determine Pr {X <= 0} c) Determine the mean of X d) Why is the previous answer fairly obvious? e) Determine the variance of X f) Compute Pr {X=2 | X >= 0} g) Determine the moment genera

Estimation : Binomial Distribution

Suppose T is a random variable such that P(T=k) = (k-1)C(r-1) * p^r * (1-p)^(k-r) (It is a negative binomial distribution.). I am trying to find the expected value E(r/T) (which is equal to r * E(1/T)) By (k-1)C(r-1) I mean (k-1)!/[(r-1)!*(k-r)!].

Statistics: Queueing Problem

A fast food outlet has an average of 8 cars at the drivethrough during "lunch rush" 11am-1pm. On average, 2 cars per min. arrive at the resaurant parking lot, and consider the drivethrough but 25% of the time, an arriving car does not actually enter the drive-through line (i.e. it "balks"). Assume no car enters the line without

Probability: Continuous Random Variables

1.) Suppose we are producing copper wire and putting the wire on spools. Each spool contains 100 feet of wire. Defects such as nicks in the wire can occur at random locations. What would be a reasonble distribution for each of the following: (a) the number of spools produced until a spool is produced that contains one or more de

Customers in a Queue

Customers arrive into a queue, where they are served, and then depart. We model the time between two successive arrivals by an exponential distribution with an arrival rate l=9. Similarly, the departure times are modeled by an exponential distribution with a departure rate m=10. Find the average number of customers in the que

Probability

I only need help with problems 1, 2, and 3. Please see the following website for the complete problems:http://www.isye.gatech.edu/people/faculty/Robert_Foley/classes/2027/hmwk3.pdf 1. Suppose that the sample space S = {1, 2, 3, ...}. Let pk = Pr({k}) for k 2 S. In each of the following cases, compute c. (a) Suppose that pk

Probability: Sample Spaces

Please see http://www.isye.gatech.edu/people/faculty/Robert_Foley/classes/2027/hmwk2.pdf for the fully formatted problems. Probability: This is where the homework 2 is found. I couldn't attach the files for some odd reason. But I ONLY NEED HELP ON PROBLEM # 2, 3, AND 4. 2. Let the sample space be S = {1, 2, 3, 4, 5}. Defi

Working with outcomes of probability.

I have been given a question to break a pin code of 5 digits, and to list all the outcomes. The numbers are between Zero and Nine. How do I go about doing this?

Probabilities from proportion tables

The following tables give the proportions of men and women in the U S population, and the proportions of men and women who have never married, in a recent year. men age proportion in population proportion never married 18-24 0.133 0.874 25-34 0.205 0.397 35-44 0.232 0.187 45-64 0.287 0.075 65 or over 0.142

Probability

You roll a dice twice. What is the probability that you will roll each of the following pairs of numbers. Please answer with explanation, and show formula. 1. 6 then 5 2. 6 then 2 or 5 3. 6 then number less than 4 4. even number then 2 or 5 5. 1 and 1 6. even number then odd number

Calculating the probability that the player wins in a game of craps.

The dice game craps is played as follows. The player throws two die, and if the sum is seven or eleven then she wins. If the sum is two, three, or twelve, then she loses. If the sum is anything else, then she continues throwing until she either throws that number again (in which case she wins) or if she throws a seven in which c

Conditional Probability Question

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. Calculate the bridge hand of 6 of one suit, 4 of another, and 3 of another.

Probability: Different Colours of Marbles

Question: A jar contains 3 white marbles, 2 yellow marbles, 4 red marbles, and 5 blue marbles. Two marbles are picked at random. What is the probability that a.) Both are blue b.) Exactly 1 is blue c.) At least 1 is blue

Probability: Considering Failure Rates

The records of Midwestern University show that in one semester, 38% of the students failed mathematics, 27% of the students failed physics, and 9% of the students failed mathematics and physics. A student is selected at random. a.) If a student failed physics, what is the probability that he or she failed mathematics? b.)

Working with probability and combinations.

There are 5 rotten plums in a crate of 25 plums. How many samples of 4 of the 25 plums contain (a) Only good plums? (b) Three good plums amd 1 rotten plum? (c) One or more rotten plums?

Calculating the probability from a given situation.

Mr. X invites 15 relatives to a party: his mother, three uncles, two aunts, four brothers, and five cousins. If the chances of any one guest arriving first are equally likely, find the following probabilities: a. the first guest is an uncle or a cousin b. the first guest is a brother or a cousin c. the first guest is an un

Using set theory to solve for the probability.

A survey of a group of military personnel revealed the following information: 95 officers 90 minorities 90 women 40 women officers 38 minority women 40 minority officers 23 women minority officers 16 caucasian male enlisted personnel How many personnel were: a. interviewed b. enlisted minority women c. male minorit