Probabilities : Craps
In a game of craps,the point is 5,what are the odds of rolling a 5 before a 7.
Probability
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Probability : Dice Roll Combinations
Find the probability when two fair dice are rolled the point is 11, given that one of the die is less than 5.
Probability : Target Shooting
An archer has probability 0.3 of hitting a certain target. What is the probability of hitting the target exactly two times in four attempts?
Probability : Random Selection
In a carnival game the players selects two coins from a bag containing two silver dollars and six slugs. Write down the probability distribution for the winnings and determine how much the player would have to pay so that he would break even, on the average, over many repetitions of the game.
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?
Determine Probability Distribution
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.
Probability : Random Selection
A man has been guessing colors of cards drawn from a standard deck of cards. During the first 50 draws he kept track of the number of cards of each color. What is the probability of guessing the color of the fifty-first card?
Use a tree diagram to determine probability. Determine the probability that a child chosen at random from the school is bussed to school.
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
Buying a new manufacturing system
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
Insurance
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
Probability: bernoulli trial model
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?
Probabilty: solve using Bayes Theorem
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
Probability, solve using methods of probability in a poker game
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
Probability
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
Six Probability Problems
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
Probability: Real World Problem Involving Random Selection
Lucky Charms has one of six different watches for prizes inside their box of cereal. If you were to purchase 60 boxes, what are the chances that you will collect all six? If you and 10 of your friends were to go purchase 10 boxes each how greater would your chances be?
Probability : Proportion Distribution Problem
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.
Probabilities : Strong Law of Large Numbers
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
Probabilities : Probability Density and Marginal Density
Please see the attached file for full problem description. --- The random vector (X,Y) has density.... where is the indicating function on that interval, i.e. it is equal to 1 if y belongs to and is equal to 0 otherwise. a. Evaluate c so that g is a probability density. b. Find the marginal densities of X and Y.
Probabilities : Marginals
A bag contains r balls, of which 2 are red and r - 2 are black. We draw a ball at random, we write down its color, and we put it to one side (not back in the bag). We repeat the procedure r times. Let X be the number of draws needed to obtain a red ball, and let Y be the number of draws needed to obtain a second red ball. a. F
Probability: Exponential Density Function
#26 Please see the attached file for full problem description. a) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probbility of failure of these bulbs by an exponential density function with mean mu = 1000. Find the probability that both of the bulbs fail in 1000 hours.
Probabilities of a Multi Facets Dice
An octahedron is a three dimensional shape with eight sides that are equilateral triangles. This shape is used as a die in games such as Dungeons and Dragons because all eight sides come up with equal probability. A. Assuming the sides are numbered 1 through 8, and a person throws two octahedral dice, what are the possible su
Policy Iteration: Probability Distribution and Maximizing Profit
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
Introduction to Bayesian Inference with examples and practical applications.
Multivariate Probability Distributions
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
Probability
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
Probability in a Table Tennis Game
FULL WORKINGS PLEASE. Clair and Helen frequently play each other in a series of games of table tennis. Records of the outcomes of these games show that whenever they play a series of games, Clair has a probability 0.6 of winning the first game and that in every subsequent game in the series, Clair's probability of winning the
Probability of Events Occurring
FULL WORKINGS PLEASE Show that the probability that exactly one of the events A and B occurs is
Probability Based on Random Selection
There are three boxes, each with two drawers. Box I has a gold coin in each drawer Box II has a silver coin in each drawer Box III has a gold coin in one drawer and a silver coin in the other. One box is chosen at random and a drawer is opened from that box. If it contains a gold coin, find the probability that it is in
Probability of Picking Groups of Cards
Find the probability that a hand of 13 cards dealt from a well shuffled pack of 52 contains: a) Exactly two kings and one ace b) Exactly one ace given that it contains exactly two kings c) Exactly 10 spades d) At least two diamonds given that it contains exactly 3 spades and 4 hearts