### Probability

Forty percent of a particular model of car are silver. What is the probability that in the next 10 observations of this model you observe 5 silver cars?

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Forty percent of a particular model of car are silver. What is the probability that in the next 10 observations of this model you observe 5 silver cars?

In a certain carnival game a player pays $1 and then tosses a fair coin until either a "head" occurs or he has tossed the coin four times. He receives fifty cents for each toss. Determine the probability distribution for the experiment of playing the game and observing the player's earnings.

Draw a tree diagram that illustrates the following. Three-fifths of kindergarten children are bussed to school, while two-fifths of the first to fifth graders are bussed. The school has grades K through 5, and 17.5% of the students are in kindergarten. Determine the probability that a child chosen at random from the school is

Company A faces the decision of buying a new flexible manufacturing system or keeping the current system. Management projections for the cash flows are given below under two demand scenarios: H (high demand) and L (low demand). This information is summarized in the following table. H(0.5) L(0.5) Old System $35M $17.5M FMS

Please see attached document. If an individual with initial wealth w that is facing a random risk X that takes values è with probability p and value zero with probability 1 - p. If the individual does not take insurance, his wealth will be w - X. If he takes insurance, his wealth will be w - a, where a is the insurance pr

Use the Bernoulli model to solve: A) Calculate probabilites of gettin from 0 to 5 clubs on a hand B) What is the probabilty of gettin 2 or fewer cubs of 5 cards?

An admissions committee must select students for an MBA program. Past data show that 70% of students complete (C) the program. It is also known that 50% of the graduating students scored above 500 (A) on the GMAT test. While 20% of the dropouts (D) scored that well. Consider a new MBA student. A) What is the prior probabilty

Poker, in the deck 52 cards, hand of 5 cards, one of the winning hands is flush, all cards belong to a common suit. A) Calculate the number of possible combinations of poker hands B) Calculate a probabilty of flush C) Calculate a probabilty of getting 4 aces on one hand D) calculate a probabilty of getting 2 aces or

In one math class of college there aer 10 males and 20 females. The professor makes 3 student teams to work on a group project. A) How many possible teams can be made? B) What is a probability that 2 females and 1 male will be in a group? C) What is a probability of 3 females only? D) What is a probabilty at least 2

1) In a survey of 125 college students, it was found that of three newspapers, the Wall Street Journal, New York Times, and Chicago Tribune: 60 read the Chicago Tribune 40 read the New York Times 15 read the Wall Street Journal 25 read the Chicago Tribune and New York Times 8 read the New York Times and Wall Street Journa

Airline company officials find that 86% of all people who make reservations show up for their flights. If an airline has accepted 240 reservations and if there are 213 available seats, find the probability that the airline will have a seat for each person who has reserved one and who shows up.

Please see the attached file for full problem description. Recall that the sequence of random variables defined on the probability space converges near-certainly towards c if and only if converges towards c) = 1. The purpose of this exercise is to prove the following result: Strong law of large numbers: Let

Please see the attached file for the fully formatted problems. 1. A machine in excellent condition earns $100 profit per week, a machine in good condition earns $70 per week, and a machine in poor condition earns $20 per week. At the beginning of any week a machine can be sent out for repairs at a cost of $90. A machine sent

Introduction to Bayesian Inference with examples and practical applications.

Please see the attached file for the fully formatted problems. Y1 & Y2 denotes the proportions of time that employee I and II actually spent working on their assigned tasks during a workday. The joint density of Y1 & Y2 is given by: f(y1,y2) = y1 + y2 , 0=<y1=<1 , 0=<y2=<1 f(y1,y2) = 0, elsewhere Employee I h

Carol and David decide to play a game as follows: Carol draws and keeps a card from a shuffled pack number 1 to 6. David the draws a card from the remaining 5. The winner is the one holding the card with the highest number. a) Determine whether or not there is an advantage to drawing the first. If the rules are no

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

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

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.

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