Explore BrainMass


Probability is a statistical measure of the chance that an event will occur.  An event, in probability, describes a set of outcomes. So for example, when two die are rolled, the events (the sums of the numbers) that may happen are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. It can be seen that 1 is not an event as a minimum of 1 must be rolled on each die. However, each event is not associated with the same probability as some of the numbers are more likely to be rolled.


For example, the sum of the numbers equaling 2 has the probability of 1/36 to be rolled – this is because there is only one combination of die rolls out of 36 which can add up to 2. On the other hand, the sum of the numbers equaling 7 has the probability of 6/36 to be rolled – this is because there are 6 combinations of die rolls out of 36 which can add up to 7. These are (1+6), (6+1), (2+5), (5+2), (3+4), (4+3).


The probability of an event is commonly written as the number of outcomes that constitute the event divided by the total number of possible outcomes, which for the number 7 is 6/36 = 1/6. Thus, it can be seen that understanding probability is a practical skill for everyday life.

Linear Programming: Minimziation of cost

Problem 2 - Dog Breeder A large breeder of a particular type of dog wishes to determine the quantities of available types of dog food that he should stock so that he can be assured that his dogs meet their nutritional requirements, but at the least cost possible. He has decided that he can do this by deciding the requirement

Some questions on normal distribution

(NOTES) calculate the z-value using the appropriate formula z=x−μ σ z=x−μ σ and find the area under the curve for z-value. Normal distribution is calculated by subtracting upper limit area from lower limit area (Round all answers to three decimal places) The mean gas mileage for a hybrid car is 57 miles per gall

BP has three potential sites where it can build a drilling rig

BP has three potential sites where it can build a drilling rig. Due to its past experience, the CEO has instructed his management team to choose no more than one site. The costs, the revenues and the estimated outcomes for each site are given in the table below. Probabilities for the different outcomes E3 (Dry) Expected re

Accuracy of Genetic Test using technique of contingency table

Acme Manufacturing Company requires all of its 5000 employees to take a drug test. Suppose 2% of the employees actually use drugs (although the company does not know this number). The drug test is 95% accurate. 1.How many of Acme's employees use drugs?. 2.How many of the employees who use drugs get a positive test result?. 3

Statistics: Frequency Distributions

I have two questions. Please use Microsoft word to write out solution. 1) The scores in Mathematics of 15 students are given below. Find range, sample variance and standard deviation. 93 85 78 79 97 90 82 61 53 63 94 69 84 67 95 Show and explain your steps. 2) The following are the prices charged (in cents)

math 540

Emily Andrews has invested in a science and technology mutual fund. Now she is considering liquidating and investing in another fund. She would like to forecast the price of the science and technology fund for the next month before making a decision. She has collected the following data on the average price of the fund during

Probability, Counting and Combination

See the attachment. 1) When dealing with probability using a dice, let's assume we have a two fair, 6-sided dice that are rolled together. a) What is the probability of the sum of the numbers on the dices to be 8 or larger? b) What is the probability of rolling a 12 on the dices? c) If one dice is red, and the oth

Statistics: Replacement and Probability

See the attachment. 6. A coin and a die are tossed. What is the probability of getting a head on the coin and a 4 on the die? Franco has a bag with four letter tiles in it. All of the tiles are the same size and shape, as shown below.(see attachment). One face of each tile has a letter on it, and the other faces are blank.

Compute the Mean and Standard Deviation of the Portfolio

An investor puts $15,000 in each of four stocks, labeled A, B, C, and D. The table below contains means and standard deviations of the annual returns of these 4 stocks. A: Mean = .15 Standard Deviation = .05 B: Mean = .18 Standard Deviation = .07 C: Mean = .14 Standard Deviation = .03 D: Mean = .17 Standard Deviation =

Compute the probability under the normal distribution

Given: 1) Invest $10,000 in Stock "ABC". 2) The daily returns are normally distributed with a mean of 0% and a standard deviation of 1%. Questions: 1) What is the probability that tomorrow's return on investment in ABC is exactly 0.9%? 2) Conditional on making a positive return tomorrow, what is the probability you make a

Probability: Possible Values

Q1. The function g: [-a,a] --> R, g(x) = sin(2(x-pi/6)) has an inverse function. The maximum possible value is a is:_____. Q2. Harry is a soccer player who practices penalty kicks many times each day. Each time Harry takes a penalty kick, the probability that he scores a goal is 0.7, independent of any other penalty kick. On

Expected Value and Law of Large Numbers in Roulette

American roulette has 38 equally sized spaces two spaces are green and have numbers 0 and 00 on them and the rest numbered from 1 to 36. Half of the non-green spaces are red and half are black. The three-number bet, also a "row bet", is a bet on the three numbers in a vertical row on the roulette table. For the three-number

Portfolio Risk Management, Systematic Risk & Unsystematic Risk

Suppose an individual investor starts with a portfolio that consists of one randomly selected stock. a. What will happen to the portfolio's risk if more and more randomly selected stocks are added? b. What are the implications for investors? Do portfolio effects have an impact on the way investors should think about the risk

Transformation of Variables in Probability Distribution

I've struggled for 3 days to come up with something approaching a relevant answer but am now desperate. Could you solve Q3, both a) and b) parts from the Exercise Sheet attached? Happy to pay 2 credits for both answers. Thank you very much. 3. The random variable X has an exponential distribution with mean µ. Let Y

Construct Confidence Intervals for Various Significances

Please help with the following: A polling company split a random sample in half and asked 477 respondents the question generally speaking, do you believe the death is applied fairly or unfairly in this country today? The pollesters asked the other 477 respondents the question, generally speaking do you believe the death penal

Confidence Interval & Margin of Error

Please help with the following: 1. Of 515 Broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of bacteria that cause food borne illnesses 85% were infected with a particular bacterium. A) Construct a 90% confidence interval? The 90% confidence interval is from _

Probability: Normal Distribution and the Central Limit Theorem

1. The weight of potato chips in a small size bag is stated to be 5 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 5.1 ounces and a standard deviation of 0.08 ounces. a) What fraction of all bags sold are underweight? b) Some of the chips are sold in "bargain

Probability Using a Frequency Table & the Central Limit Theorem

1. You roll a die, winning nothing if the number of spots is odd, $3 for a 2 or a 4 and a $18 for a 6. a) Find the expected value and standard deviation of your prospective winnings b) You play three times. Find the mean and standard deviation of your total winnings. c) You play 60 times. What is the probability that you wi

Computing a Payoff Table and Finding an Optimal Decision Using Given Data

Jim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold Key is offering him one of three salary plans for the next year: (1) a 25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a s

Examples of Independent and Dependent Variables

1) A company that sells different types of slippers wants to see how their new line of comfortable walking slippers sells so the company keeps changing the price on this certain product several times to find the best price for it. The company records the quantity it sells for each price level and then performs a linear reg

Basic Statistics: Mean, Standard Deviation, Probability, Normal Distribution

1) Adult American males have normally distributed heights with a mean of 5.8 feet and a standard deviation of 0.2 feet. What is the probability that a randomly chosen adult American male will have a height between 5.6 feet and 6.0 feet? A. 0.6826 B. 0.5000 C. 0.9544 D. 0.7500 2) A jar contains 12 red jelly beans, 20 yell

Regression & Residual Analysis

An experiment was carried out to assess the impact of the variables x1 = force(gm), X2 = power (mW), x3 = temperature (C) and x4 = time (msec) on y = ball bond shear strength (gm). The results are given in the problem 5 Excel data file. a. Perform a complete analysis. b. Perform a complete residual analysis. c. Check for col

X-bar and R-Chart

The dataset contained in the problem #4 Excel file gives data on moisture content for specimens of a certain type of fabric. a. Create an X-bar R chart, using the first 10 subgroups as the base period. Comment on what is shown. b. What did you assume to construct these control limits (be specific)? Check the assumptions.

steps on performing a 3-factor factorial design

1. An experiment was designed to see what factors affect the cleaning ability of a washing solution. Three factors were used in the experiment - the concentration of detergent, concentration of sodium carbonate, and concentration of sodium carboxymethyl cellulose. A larger value of the response indicates better cleaning abilit

Computing probability using the Rule of Addition

In our virtual world, we own a construction company and bid on projects. Based on our past history of winning bids on projects, the probability of winning the next contract to build a school is 0.40, to build a hospital is 0.30 and to build both a school and a hospital is 0.20. What is the probability of winning a contract to bu

History of Statistics

Describe the historical development of statistics and probability In non-Western cultures