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A jar contains marbles of different colors: 4 white, 6 black, 6 red, and 4 blue. On two random drawings, without replacement, find the probability that the first is black and the second is white. Assume that the draws are independent.


Take a deck of cards. A deeck has 52 cards with two major colors(Red and Black), with 26 cards each. Red colors comes in two shapes(heart and diamond), while black color shapes are called clubs and spades. Find the probability of obtaining Red or Queen. That is, find Probability(Red or Queen).

Probability problem...

How many ways can 6 distinguishable balls be placed in 5 boxes such that there are 2 balls in the first box, and one in all remaining boxes?

Probability bounds using Chebychev's inequality

Many people believe that the daily charge of a price of a company's stock on the stock market is a random variable with mean 0 and variance {see attachment}. That is, if Yn represents the price of the stock on the n-th day, then (see equation in attachment( where X1,X2,..., are independent and identically distributed random var

Normal Probability Distributions

Suppose the lifetime income of all high school grads is normally distributed and that the lifetime income of all college grads is normally distributed. Suppose that the difference in the means is known to be $600,000 and that the standard deviation of the high school graduates is $300,000 and the standard deviation of the colle

Probability for the Skateworld Company

The Skateworld Company operates ice rinks in several major cities throughout the United States. During each session of open skating, one customer is selected at random to receive a free pass for a future open skating session. At a recent session there were 150 males and 130 females skating. What is the probability that the pe

Random number sets

1. Choose a number at random from the set of numbers from the set of numbers {1,2,3,4,5}. Now choose a number from the subset {1,...,X). Call this second number Y. a) Find the joint p.m.f. of X and Y b) Find the conditional mass function of X given that Y = i. Do it for i = 1,2,3,4,5 c) Are X and Y independent? Why?


Subject: Probability Details: You appear on a game show and for your prize the host lets you choose one of three doors. Behind one door is a new car; behind each of the other doors is a goat. You choose a door. The host, who knows what's behind each door, then opens another door, which has a goat. He then asks if you want to p

Exponential random variable

I)Let X be an exponential random variable with mean 1,and Y = exp^(X/2): a)find F(y) b)Evaluate E(Y) c)Evaluate E[(Y^2)/(1+(X^2))] II)The random variable X is uniformly distributed on the interval [1,3].Find the probability density function fy(y)of the random variable Y=2X+5

Proportion and Probability

According to hypothetical information, 18% of all Americans have hazel colored eyes. A SRS of 25,000 Americans are surveyed and asked about their eye color (assume each of the Americans in the sample has an 18% chance of having hazel colored eyes). a) Determine the mean and standard deviation of this sample of Americans that


The scores of students taking the Scholastic Aptitude Test (SAT) are normally distributed with a mean u = 1035 and a standard deviation o = 131. a) Determine the probability that a simple random sample of 15 students would earn an average score of 1000 or less. b) Determine the probability that a simple random sample

Statistical probability

The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by f(x) = (ax2e&#8722;bx2 x>_0 { 0 x < 0 where b = m/2kT and k, T and m denote, respectively, Boltzmann's constant, the absolute temperature, and the mass of the molecule. Evaluate a i

Cumulative distribution function (same as 26793)

A cdf Fx is stochastically greater than a cdf Fy if (1) Fx(t)<= Fy(t) for all t, and (2) there exists some t for which Fx(t) < Fy(t) (a)show that if Fx is the cdf of X and Fy is the cdf of Y, then (1) P(X>t) >= P(Y>t) for all t and (2) P(X>t) > P(Y>t) for some t.(in other words, X tend to be bigger than Y) Give an example.

Statistics: Probability

The prizes that can be won in a sweepstakes are listed below with the chances of winning each one: $4000 (1 chance in 8200); $1700 (1 in 5300); $800 (1 in 4100); $200 (1 in 2200). Find expected value of the amount won for one entry if the cost to enter is 55 cents. Answer is 0.54. Please explain the procedure (without only showi

Probability Applied to Genetics

You are reviewing a scientific study where the epidemiologists sampled 1000 people from Charleston, South Carolina and measured variation at two loci, A and B. The haplotype frequencies in the sample population are: AB = 0.406 Ab = 0.214 aB = 0.214 ab = 0.166 Toward the end of the article you are reviewing, you read tha

Statistics - variance and expectation

It has been determined empiracally that for a certain egg producer, the number of cracked or broken eggs X, in a randomly slected box containing six eggs, follows approximately the distribution given in the table below: X: 0 1 2 3 4 5 6 P(X): 0.9 0.07 0.02 0.005 0.003 0.001 0.001

Probability: Color Smart Television Sets

The manufacturer of the ColorSmart-5000 television set claims that 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 consumers who have owned a ColorSmart-5000 television set for five years. Of these 400 consumers, 316 say that thei

Mathematics for Computing Solutions

I have completed these but have no solutions with workings out Use the binomial distribution to calculte the pobability of........Calculate the probability that the lifetime of a paticular device is........Investigate the degree of correlation between the results....Use a regression technique to estimate the job performance..




Question 1 (5 points) Chose a simple random sample of size five (5) from the following employees of a small company. 1. Bechhofer 4. Kesten 7. Taylor 2. Brown 5. Kiefer 8. Wald 3. Ito 6. Spitzer 9. Weiss Use the numerical labels attached to the names above and the following list of random digits. Read the

Analysis and Decision Tree

Techware Incorporated is considering the introduction of two new software products to the market. In particular, the company has four options regarding these two proposed products: introduce neither product, introduce product 1 only, introduce product 2 only, or introduce both products. Research and development costs for prod


Suppose you roll a die. If you roll an odd number, you win the dollar amount corresponding to the number of dots showing. If you roll an even number, you lose the number of dollars corresponding to the number of dots. (For example, if you roll a three you win $3. If you roll a six, you lose $6.) You pay $.50 (fifty cents) t

Binomial Distribution

1.If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability that all 3 cards are queens. 2. A fair coin is tossed 8 times in succession. Find the probability of getting at least 4 heads. 3. A die is rolled twice. Find the probability of getting two numbers whose sum exceeds 5. 4.How many different five-l

Probability Distribution Function

Suppose that the random variable y is described by the following probability distribution function: f(y) = 2/9y for 0<or=y<or=3 and it is 0 elsewhere. a.) Find P(0.50<or=y<or=1.50) b.) Find the mean and variance of y.


A study of vehicle flow characteristics on acceleration lanes found that one out of every six vehicles uses less than 1/3 of the acceleration lane before merging into the traffic. Suppose we monitor the location of the merge for the next 5 cars that enter the acceleration lane. a.)What is the probability that none of the veh

Probability questions

a)Probablity an event is likely to occur? b) P of an impossible event? c) Sample space consists of 25 separate events equally likely. What is P of each? d) True/False test. P of correct if a random guess? e)Multiple choice test with 5 possible answers for each, P of getting correcdt of random guess?