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# Probability

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### Simple Probability and Intersection Laws

The question that I am uncertain of is as follows: If P(A/B) = .2 and P(B^c) = .6, then P(B/A) is .8 .12 .33 cannot be determined

### Probabilities Applied to Sodas

I am having problems with this question: Super Colas sales break down as 80% regular soda and 20% diet soda. While 60% of the regular soda is purchased by men, only 30% of the diet soda is purchased by men. If a woman purchases Super Cola, what is the probability that it is a diet soda? The choices are .28902 .30435 .69

### Gamma Distribution and Probability Density Function

Suppose the X1 and X2 denote a random sample of size 2 from a gamma distribution, (see attached file). This is Gamma distribution. a) Find the pdf (probability density function) of Y = (X1 + X2)^1/2 b) Find the pdf (probability density function) of W = X1/X2 In this problem you have to find for the pdf in part a and b, th

### Solving Variables: Example Problems

(See attached file for full problem description with proper symbols) We are using the book: Introduction to probability and mathematical statistics by Bain Engelhardt. Let X and Y have joint pdf and zero otherwise. a) Find the joint pdf of U=X/Y and V=X b) Find the marginal pdf of U

### Discovering the Probabilities

I know that the probability is .025 that an applicant at my bank will not be able to an installment loan. Last month we made 40 loans. A. What is the probability that 3 loans will be defaulted? B. What is the probability that at least 3 loans will be defaulted?

### Statistics Probability Problem

Be sure to show all work 1. The Masterfoods company says that before the introduction of purple, yellow candies made up 20% of their plain M&M's, red another 20%, and orange, blue, and green each made up 10%. The rest were brown. If you pick an M&M at random, what is the probability that: a. it is brown? b. it is yel

### Poisson Distributions

Assume the accidents occur at random according to a Poisson process a rate of one every two days. a) What is the probability that exactly two accidents will occur in a particular two-day interval? b) What is the probability that one will have to wait at least two days to observe the next two accidents? --- I do not und

### Using Poisson and Binomial Distribution

The random variable X has a Poisson distribution with a mean of 5. The random variable Y has a binomial distribution with n=X and p=1/2. a) Find the mean and variance of Y. b) Find P(Y=0)

### Normal Distribution and Patient Waiting Times

I need some help with this statistics question: The Director of Emergency Medicine at NYU Hospital is studying patient waiting times. "Waiting time" is defined as the time from when a patient enters the facility until he or she is seen by a physician. The study indicates that waiting time follows a normal distribution with a

### Random Variables for Marbles

One box contains five red and six black marbles. A second box contains 10 red and five black marbles. One marble is drawn from box 1 and placed in box 2. Two marbles then are drawn from box 2 without replacement. What is the expected number of red marbles obtained on the second draw?

### Decision making

Decision making under risk is a probabilistic decision situation. True False The several criteria (maximax, maximin, equally likely, criterion of realism, minimax) used for decision making under uncertainty may lead to the choice of different alternatives. True False One disadvantag

### Binomial Distribution Scenarios

In each situation below, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. (a) An auto manufacturer chooses one car from each hour's production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples, ripples, scratc

### Probabilities & Decision Making for a Winery

I need help with the following question set: A winery purchased land for establishing a new vineyard. Management is considering 2 varieties of white grapes for the vineyard: Chardonnay & Riesling. The Char. grapes would be used to make a dry wine and the Riesling grapes would be for a semi-dry Riesling wine. It takes almost

### Optimistic, Conservative & Minimax Regret Approaches

Which approach is most preferred and why? Optimistic, conservative, or minimax regret. Also, is establishing the most appropriate approach before analyzing the problem important for the decision maker? Explain.

### Binomial Distribution

Given: probability of hypertension is 0.15 What is the probability that out 3 out of 17 patients have hypertension: at most 2 patients have hypertension at least 3 patients have hypertension

### PDF of processors

(See attached file for full problem description with full equations) --- 1. In a computing facility there are two types of processors: type A and type B. Suppose random variable X represents the processing time of a job. With type A processor, the processing time has PDF: and with type B processor it is: Also

### What are the steps for using the Normal Table for finding Probability problems?

What are the steps for using the Normal Table to find the following: a. The Probability steps for (z<-2.65) b. The Probability (z>-1.55) c. The Probability (-2.00<z< 2.25) d. The Probability (1.25<z<2.40)

### Calculating Probabilities of finding oil

I need help with the following questions. Please show your work so I can practice with other problems. Thank you An oil company purchased an option on land in Oklahoma. Preliminary studies assigned the follwing prior probabilities. P(high-quality oil) = .50 P(medium-quality oil) = .20 P(no oil) = .30 a. What is t

### Calculating Probabilities

Please show work so I can learn how to do this. (See attached file for full problem description) --- I need help with the following. Please show work so I can learn how to do this. A study of job satisfaction was performed for 4 occupations: doctor, chemist, CPA, & dentist. Job satisfaction was measure

### A six-sided die is rolled...

A six-sided die is rolled 30 times and the numbers 1 through 6 appear as shown in the following distribution... (See attached file for full problem description)

### Chevalier de Mere's puzzle and other questions of probability

(See attached file for full problem description) --- 1. Chevalier de Mere's puzzle (Scandal of Arithmetic) Consider two experiments: a. Roll a fair die 4 times. Record the number on top. b. Roll a pair of fair dice 24 times, record the pair on top. For experiment a, find the probability of event A: at least one

### Financial Decision-Making : Borrowing Decisions Simulation and Simulation Based Cash-Budgeting

Help me understand questions that reflect the borrowing decisions simulation.

### Calculations with Mean and Standard Deviation

The verbal part of the SAT has a mean of 500 and a standard deviation of 100. If we randomly selected 1500 students who had taken the the verbal SAT how many would score lower than 250?

### Probability of Being Contacted in an Emergency

Jules, Vincent, and Mia are physicians at the local hospital. One of their duties is being on call during non-working hours to handle any emergencies that might come up. Each carries a pager that can be activated by hospital personnel. Suppose Jules responds to his pager 80% of the time, Vincent responds to his pager 55% of the

### Probability Distribution for a Basketball Game

Please calculate the probability distribution and answer questions a and b At the end of a basketball game, a team is down by 1 point. As the last play, a player from that team throws a three-point shot that misses, but the player is fouled and he gets to take 3 free throws (each worth 1 point) to end the game. On any given f

### Probability of Winning a Basketball Game

At the end of a basketball game, a team is down by 1 point. As the last play, a player from that team throws a three-point shot that misses, but the player is fouled and he gets to take 3 free throws (each worth 1 point) to end the game. On any given free throw, the probability that the player makes the shot is twice as large as

### Probability Code Possibilities

Secured doors at airports and other locations are opened by pressing the correct sequence of numbers on a control panel. If the correct panel contains the digits 0-9 and three digit code must be entered (repetition is permitted) a) How many different codes are possible? b) If one code is entered at random, find the prob

### Probability of Selecting Certain Marbles from a Bag

A box contains 4 marbles: 2 red, one blue and one green. Two marbles will be selected at random. Find the probability of selecting each of the following. A) with replacement B) without replacement i A red marble and then a blue marble ii Two blue marbles iii No red marbles iv No green marbles.

### A TV remote has keys for channels 0-9...

A TV remote has keys for channels 0-9. If you selected one key at random. a. What is the probability that you press channel 3? b. What is the probability that you press a key for a even number channel? (Assume 0 is even) c. What is the probability that you press a key for a number less than 7?

### Empirical Probability of Guinea Pigs

An experimental serum was injected into 500 guinea pigs. Initially, 150 of the guinea pigs had circular cells, 250 had elliptical cells, and 100 had irregularly shaped cells. After serum was injected, none of the guinea pigs with circular cells were affected, 50 with elliptical cells were affected and all of those with irregul