Explore BrainMass


Probability is a measure of how likely it is for an event to take place. Probabilities are often denoted by a value ranging between 0 and 1, where 0 represents an impossible event, while 1 represents an event that will definitely happen. Therefore, in this context, the higher the degree of probability, the more likely the event is going to happen.

Before the probability of an event can be computed/measured, the sample space, denoted by the sign Ω, represents the set of all possible outcomes of a random variable. Events in probability are usually denoted by a letter. So for a given set of outcomes, the event may be labeled ‘A’; for another given set of outcomes, the event may be labeled ‘B’. In light of this, an event, either ‘A’ or ‘B’ is a subset of the sample space.

In probability, there are other symbols used to describe composite events. The ∪ sign in A ∪ B denotes the union of two events. So A ∪ B denotes a composite event that occurs if either A or B occurs, or they both occur. The ∩ sign in A ∩ B denotes the intersection of two events. So A ∩ B denotes a composite event that occurs if both A and B occur. The A’ sign denotes an event that cannot occur with A. But one of A’ and A must occur.

These concepts are used widely in an ever expansive area of study, such as mathematics, statistics, epidemiology and even philosophy. Thus, understanding the concepts of probability may prove to be a practical tool for anyone.

Categories within Probability

Probability Density Function

Postings: 92

Probability density function describes the probability of a random variable taking on a specific value.

Cumulative Distribution Function

Postings: 22

Cumulative distribution function refers to the probability of a random variable X, being found lower than a specific value.

Central Limit Theorem

Postings: 98

The Central Limit Theorem is a statistical theory which describes a situation where the mean of all samples from the same population will approximately equal the mean of the parent population, given that the sample size is large and that the variance is finite.

Geometric Probability

Postings: 9

Geometric Probability refers to the probability involving geometric objects under stated conditions.

Bayesian Probablity

Postings: 53

Bayesian probability refers to the probability of an event given a level of certainty of an external factor relating to that event.

confidence interval and Z

A local university administers a comprehensive examination to the candidates for B.S. degrees in Business Administration. Five examinations are selected at random and scored. The scores are shown below. Grades 80 90 91 62 77 I am interested in the overall performance for all candidates of a B.S. degree. The populati

Game Theory Critical Thinking

Given the following payoff matrix, ( a) indicate the best strategy for each firm. ( b) Why is the entry-deterrent threat by firm A to lower the price not credible to firm B? ( c) What could firm A do to make its threat credible without building excess capacity? (Refer to Tables Sheet) NOTE: P10(a):The strategies for firm A

Measure of Central Tendency

Question 1 A family member can go to one of two local hospitals for brain surgery. Checking the history for the past year, you find that each of the two hospitals has performed brain surgery on 1000 patients. In hospital A 710 patients survived (71%). In hospital B 540 (54%) survived. Based on the numbers presented, which ho

Normal distribution analysis

Maximum and Minimum Temperatures Search the Internet for U.S. climate data. Choose the city in which you live. Click on the tab that reads "Daily." 1. Prepare a spreadsheet with three columns: Date, High Temperature, and Low Temperature. List the past 60 days for which data is available. 2. Prepare a hist

NPV Investment Opportunity

Scenario: You are an entrepreneur that has several business investments in real estate, restaurants, and retail stores. You are looking for your next investment opportunity for you and your private equity investment company. You have found two possible alternatives to invest in that will payoff in the next 10 years. Here are the

Running for Office Polling Probability Worksheet

New Competencia Demographic Data 1. Assuming no calls have been made to New Competencia residents yet, what is the probability that the first phone call will be to someone in McGovern's target population? 2. A few hours into your visit, the polling center has called 37 small business owners, 63 residents between ages 18-

Normal Approximation in the Binomial Distribution

The next North Carolina gubernatorial election will be held in 2016. Suppose that 52% of North Carolina voters actually support Candidate A in that election. a) What is the probability that a poll of a simple random sample of 100 NC voters will result in at least half of those polled favoring the other candidate? Use the no

Home Free General Contractor Game Show

Game Overview ● There are 15 toolboxes, each holding a prize of a set value. ● As the contestant, you must begin the game by randomly select one toolbox. The value hidden in this toolbox is what you will win if you choose to keep it throughout the game, but you will have multiple chances to trade it in for a guaranteed pri

Confidence intervals using normal distribution

Mimi was the 5th seed in 2014 UMUC Tennis open that took place in August. In this tournament, she won 80 of her 100 serving games. Based on UMUC sports Network, she wins 75% of ;the serving games in her 5 year tennis career. 1. Find a 90 % confidence interval estimate of the proportion of serving games Mimi won. (Show work an

Determine the birthplace of a class of college students.

A poll was taken to determine the birthplace of a class of college students. Below is a chart of the results. a. What is the probability that a female student was born in Orlando? b. What is the probability that a male student was born in Miami? c. What is the probability that a student was born in Jacksonville? Gender

Normal Distribution and Probability

The Nordic Ecolabel is the official Ecolabel of the Nordic countries and was established in 1989 by the Nordic Council of Ministers.The Nordic Ecolabel evaluates a product's impact on the environment throughout the whole life cycle. The label guarantees among other things that climate requirements are taken into account, and tha

Probability for Gender and Major

Create a pivot table of Gender and Major. Then complete the Joint Probability table so you can answer the following: a) What is the probability of randomly choosing a Female? b) What is the probability of randomly choosing a Male AND Finance major? c) What is the probability of randomly choosing a Female OR Leadership maj

Normal Distribution and Verification of Data Distribution

Number Of Hours Of Television Watched 36.1 30.5 2.9 17.5 21.0 23.5 25.6 16.0 28.9 29.6 7.8 20.4 33.8 36.8 0.0 9.9 25.8 19.5 19.1 18.5 22.9 9.7 39.2 19.0 8.6 Using the following normal probability plot, determine if the data could have come from a normal distribution. Normal Probability Chart Determine the mean and st

Normal Probability Using the Z Score

1) The average amount of participation in Dallas, Texas, during the month of April is 3.5 inches Assume that a normal distribution applies and that the standard deviation is .8 inches. What percentage of the time dose the amount of rainfall in April exceed 5 inches? What percentage of the time is the amount of rainfall in Ap

Normal Probability Distribution and Confidence Intervals

What is the probability of P(-1.4 < Z < 0.6)? In a standard normal distribution, what is the area which lies between Z = -1.72 and Z = 2.53? Use the following information to conduct the confidence intervals specified to estimate μ. 95% confidence; X ̅=25, σ^2= 12.25, and n=60. 30% confidence; X ̅=119.6,

Hypothesis Testing: Normal Probability Distribution

Consider the following hypothesis test: Ho (null hypothesis): µ = 15 Ha (alternative hypothesis): µ ≠ 15 A sample of 25 gives a sample mean of 14.2 and sample standard deviation of 5. Answer the following questions regarding the hypothesis test. a) At α = 0.05, what is the rejection rule? b) Compute the value of

An Introduction to Descriptive Statistics and Probability

Please include all steps. 1) In a poll, respondents were asked if they have traveled to Europe. 68 respondents indicated that they have traveled to Europe and 124 respondents said that they have not traveled to Europe. If one of these respondents is randomly selected, what is the probability of getting someone who has travel

Counting, probability and normal probability plot

(a) The financial database of a company is secured by a password protection system. Each employee is given a randomly generated password containing three letters and two numbers. If repetitions of letters and numbers are not allowed, how many possible passwords are there? (b) Tickets for international cricket matches betw

Computing Normal Probabilities with a Given Z Score

1. Given that z is a standard normal random variable, compute the following probabilities. a. p (z = 2.0) b. p (z ≥ 1.4) c. p (-1.0 < z < 0.5) d. p (1.0 < z < 1.2) 2. The time needed to drive from city A to city B is normally distributed with a mean of 180 minutes and standard deviation of 20 minutes. a. Wha

Exercises with Z-Scores and Percentiles

Six steps of hypothesis testing are: Identify populations, comparison distribution, and assumption; state null and research hypothesis; determine characteristics of the comparisons distribution; determine critical values, or cutoffs; calculate test statistic; and make a decision. Question 7.18: Calculate the following p

Null and Alternative Hypotheses and Type I and II Errors

Share the null and alternative hypotheses for a decision that is relevant to your life. This can be a personal item or something at work. Be sure that it is mathematical in nature. Additionally, identify the Type I and Type II Errors that could occur with your decision‐making process. Be sure to quantify your hypotheses as mu

Computing Probability and Deciding Extreme Samples

Please explain how to solve. I have attempted to answer, please let me know if I'm right or wrong. Thank you! a random sample of n=9 scores is selected from a normal distribution with u= 80 and o=12. what is the probability that the sample mean will be between 76 and 84? * 0.9974 *0.3830 * 0.2586 * 0.6426 ( is this correc

Sample Mean and Population Mean: Standard Deviation

Please explain how to set up and solve. I have attempted to answer, please let me know if right or wrong... A sample of n= 36 scores is selected form a population with o= 12. if the sample mean of M=56 produces a z score of z= +3.00 then what is the population mean? * 56 *52 (is this correct?) * 54 *50 A sample of n=

Tattoos and Attractiveness

There is some evidence indicating that people with visible tattoos are viewed more negatively than people without visible tattoos. In a similar study a researcher first obtains overall ratings of attractiveness for a woman with no tattoos shown in a color photo. On a 7 point scale the woman receives an average rating of u= 4.9,

Hypothesis Testing for One Sample Z Test

There is a popular belief that herbal remedies such as ginkgo biloba and ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well controlled research. in a typical study a researcher obtains a sample of n=16 participants and has each person take a herbal supplement for 90 days. a

Standard Error calculations for population

A population has a standard deviation of o=20, how large a sample is necessary to have a standard error that is: Less than or equal to 5 points? n>______ Less than or equal to 2 points? n>______ Less than or equal to 1 point? n>______ If I have a sample of n=25 scores, what is the value of the population standard devi

Descriptive Statistics, Confidence Interval & Testing

Bottling Company Case Study /Calculate measurements of central tendency and dispersal. Determine confidence intervals for data. Imagine you are a manager at a major bottling company. Customers have begun to complain that the bottles of the brand of soda produced in your company contain less than the advertised sixteen (16)

Probability: expected value using exponential distribution

Please assist in answering the following question. Please submit details of work including excel sheet used to arrive to the solution. Provide interpretation of results and describe conclusions. 1. Suppose that a car rental agency offers insurance for a week that will cost $10 per day. A minor fender bender will cost $1,500,