A hat contains n coins, f of which are fair and b of which are biased to land on heads with a probability of 2/3. A coin is drawn from the hat and tossed twice. The first time it lands heads and the second time it lands tails. Given this information, what is the probability that a fair coin has been chosen?
Four couples, each consisting of one man and one woman, are seated at a circular table. Assuming that each different order is equally likely, find the probability that: a) Andrew is sitting next to his partner b) Benjamin, Charles and David are sitting together (in any order) c) The men and women sit alternately
Please could I have the answer to this: Full workings please. A shortlist of 10 people is drawn up from a large number of applicants for a certain job. The shortlist consists of 7 men and 3 women. Because all the shortlisted applicants are considered to be equally qualified, the names of two of them are drawnn, one afte
A particular type of electronic component for use in PCs is mass produced and subject to quality control checks since it is known that 2% of all components produced in this way are defective. The quality of a day's output is monitored as follows. A sample of 10 components is drawn from the day's output (which may be assumed to
1) A drawer contains n=5 different and distinguishable pairs of socks (a total of 10 socks). If a person randomly selects 4 socks, what is the probability that there is no matching pair in the sample? 2) A drawer contains n different and distinguishable pairs of socks (a total of 2n socks). A person randomly selects 2r o
My uncle plays darts on a circular dart board of radius 20 cm. He assumes a dart lands anywhere on the board with equal probability. a) What is the probability that his dart lands less than 5 cm from the centre of the board? b) That his dart lands exactly 5 cm from the centre? c) My uncle wants to divide his board into ten
Q. The 'cup' system for determining the champion amongst 2^n players consists of drawing lots to arrange the players in 2^n-1 pairs who are to play each other, then repeating this with the 2^n-1 winners of these matches, and so on. The winner and loser of the final match recieve the first and second prizes repectively. Suppose
A mouse, after being placed in one of 4 rooms, will search for cheese in that room. If unsuccessful, after one minute it will exit to another room by selecting a door at random. (All the rooms connect to each other.) A mouse entering the room with the cheese will remain in that room. If the mouse begins in room 3, what is the pr
2.) Suppose X has probability mass function Pr{X = k} = c(k + 2) for k = -1, 0, 1, 2 . Find c, and compute the mean, variance, and standard deviation of X. Let Y = 3X + 5. Compute the mean, variance and standard deviation of Y
) Let X and Y have joint probability density function f(x,y) (s,t) = ce ^ -(s + 2t) for 0 <= s, and 0 <= t. Find (a) c (b) Pr {min (X, Y) 1/3} (c) Pr {X <= Y} (d) The marginal probability density function of X (e) E [XY] 5) Let X and Y be independent uniform (0,1) random variables. Compute (a) Pr {X < Y} (b) Pr {X
If a die is rolled 4 times, what is the probability that a 3 comes up at least once?
Determine the number of people needed to ensure that the probability at least two of them have the same day of the year as their birthday is at least 70 percent, at least 80 percent, at 90 percent, 95 percent, at least 98 percent, and at least 99 percent.
Suppose you roll two dice a) What are the odds in favor of rolling a sum of 10? b) What are the odds against rolling a sum of 7 or 11? c) In part a, if you bet one dollar that a sum of 10 will turn up, what should the house pay (plus returning your one dollar bet) if a sum of 10 turns up for the game to be fair?
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
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?
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?
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
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
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 - - - - - - - -
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
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
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
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
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
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)!].
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
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 Pr{x <= 0} (b) Determine the mean of X (c) Determine all medians of X (d) Compute Pr{X=2 | X >= 0} (e) Determine the cumulative distribution function
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 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
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