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Probability : k-out-of-n System

2.54) Consider the k-out-of-n system (explanation: a system consists of n independent components. Each component functions with probability p. The system as a whole functions if at least k components are functioning (1 <= k <= n)). Suppose we visit this system at time t=3 and replace all failed components, at a cost of $75 eac

Probability : Random Selection

Suppose there are two vendors and each provides 50% of the items. The lifetime (in days) of an item from the first vendor is Exp(.1), and that from the second vendor is Exp(.08). Compute the probability that a randomly picked item will last more than 12 days.

What is the probability that the kth shock kills the machine?

2.20) Suppose a shock causes a unit damage to the machine with probability 0.1 and no damage with probability of 0.9. Successive shocks are independent. Suppose the damages are cumulative and the machine can withstand at most four units of damage. (That, is the machine fails when the fifth unit of damage is inflicted on it.) Wha


2.16) Consider the k-out-of-n system (info on the system: A system consists of n independent components. Each component functions with probability p. The system as a whole functions if at least k components are functioning (1 <= k <= n)). The probability that a component is functioning at time t is given to be e^(-t). Comput

Probability using Bayes theorem

1.22) An oil executive has determined that the probability that this oil field contains oil is 0.6. Before starting the drilling she decides to order a seismological test to see if there is oil in the ground. Unfortunately, the test is not entirely accurate. It concludes that there is oil with probability 0.9 if there is indeed


In the questions I have below it says a bowl has eight ping pong balls numbered 1,2,2,3,4,5,5,5. You pick a ball at random. a. Find p(the number on the ball drawn is &#8805; 3). b. Find p(the number on the ball drawn is even).


A jar contains 8 red marbles, 9 blue marbles, and 6 green marbles. Two marbles are chosen at random. What is the probability that one is green and the other is blue?


Let E and F be non-zero-probability events. If E and F are mutually-exclusive, can they also be independent? Explain the answer, and also prove it algebraically using the definitions of mutually-exclusive and independent events.


If E and F are events with P ( E U F ) = 5/8, P (E &#8745; F = 1/3, and P (E) = ½, Find: (a) P(E) (E has a straight line over it) (b) P (F) (c) P (F) (F has a straight line over it) detail each answer: (a) ½ (b) 11/24 (c) 13/24


An experimental test to detect a particular type of cancer indicates the presence of cancer in 90% of individuals known to have this type of cancer, and in 15% of individuals known to be cancer-free (false positive). One hundred individuals volunteer to take the test. Of the 100, 60 are known to have the cancer, and 40 are known

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.


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.


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


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 : 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.