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# Probability

### Probability Problems: Colored Candy Example

Use the theoretical method to determine the probability of the given outcome or event. A bag contains 5 red candies, 15 blue candies, and 20 yellow candies. What is the probability of drawing a red candy? a blue candy? A yellow candy? Something besides a yellow candy? The probability of drawing a red candy is ______ (round t

### Expected Value: Lottery

A magazine ran a sweepstakes in which prices were (see list below). listed along with the chance of winning. values 1 chance out of \$1,000,000 ; 80,000,000 \$100,000 ; 120,000,000

### Die throw problem

We repeatedly throw a die, stopping when the value of the throw exceeds the value of the first throw. Compute the expectation value of the number of throws.

### Binomial and Poisson Distributions in Real Life

Examples of the binomial and Poisson distributions are all around us. - Identify a real-life example or application of either the binomial or poisson distribution. - Specify how the conditions for that distribution are met. - Suggest reasonable values for n and p (binomial) or mu (poisson) for your example. -

### Poisson distribution

Q1: A sample of n independent observations x1, x2, . . . , xn are obtained of a random variable having a Poisson distribution with mean ?. Show that the maximum likelihood estimate of ? is the sample mean [see the attached file]. Show that corresponding estimator (X) is an unbiased estimator of ?, and has variance ?/n.

### Solving Probability Problems

Assume that the average number of traffic accidents requiring medical assistance between 7 and 8 AM on Wednesday mornings is 1. What then is the chance that there will be a need for exactly 2 ambulances during that time slot on any given Wednesday morning?

### Probability Concepts and the Standard Normal Distribution

Hi, I need some assistance with the following two questions. I am not sure that I understand the questions fully. Any assistance would be appreciated. 1. What are some conditions under which business decisions are made using probability concepts? Provide at least two examples of subjective probability. 2. What are the chara

### "What are the odds...?"

Assume that the Wheel of Fortune has 24 slots, each subtending 15 degrees. There are two bankrupt slots. 1. Assuming each spin has a random result, what are the odds of hitting a bankrupt slot? 2. a) Does the layout of bankrupt slots impact this result? b) Explain your answer.

### Diffusion as a Probability

Diffusion as a probability for a random walk - please see the attached question. No big derivation is required and this may be able to be answered in just a few lines. The main point is to show the probability of hopping using only the values given at the bottom of the attached pdf.

### Probability of drawing apples from a sample

There are 8 spoiled apples in a container of 27 apples set for inspection. A sample is drawn, for 4 apples at random, from the container during inspection. a) How many ways can the 4 apples be drawn in which there are 1 good apple and 3 spoiled apples? b) How many ways can the 4 apples be drawn in which none are spoiled? c)

### Probability in Situations Given

A company that has 327 employees chooses a committee of 17 to represent employee retirement issues. When the committee was formed, none of the 83 minority employees were selected. 1. Find the number of ways 17 employees can be chosen from 327. 2. Find the number of ways 17 employees can be chosen from 244 non-minorities. 3. I

### Mutually Exclusive events, Probabilities, and Binomial Distribution

1. Are the events mutually exclusive (Yes or No)? Event A: Randomly select a person between 18 and 24 years old. Event B: Randomly select a person that drives a convertible. 2. Decide if the events are mutually exclusive. Event A: Randomly select a person who uses email. Event B: Randomly select a person that uses social

### Odds of winning

You are given 9 to 1 odds at tossing 3 heads in a row with three coins; meaning you win \$9 if you succeed and lose \$1 if you fail. a) Find the expected value (to you) of the game. b) If you play one game would you expect to win or lose the game? Explain. c) What about if you play 100 games?

### Empirical Probability: Coin Toss

Use the empirical method to estimate the probability. You count 42 heads when you toss a coin 100 times. If you don't know whether the coin is fair what is the probability the next toss will be a tail?

### Deck of cards probability

A standard deck of 52 cards is shuffled (all possible orderings are equally likely) and the cards are turned up one at a time. What is the probability that all the aces will appear before any of the tens?

### Probability: Calculating the Expected Value

You give \$3 for a bet in a casino game and there is a 253/495 probability that you will lose your \$3 and there is a 242/495 probability that you will make a net gain of \$3 (If you win the casino gives you \$3 and you keep your \$3 bet so the net gain is \$3). 1. What is your expected value? 2. In the long run how much do you

### At Least Once Probability

Use the at least once rule to find the probability of the following event. Drawing at least one black card when you draw a card from a standard deck 6 times, replacing the card each time you draw so that there are always 52 cards in the deck.

### Probability: Length of Machine Produced Metal Strips

Length of metal strips produced by a machine are normally distributed with mean length of 150 cm and a standard deviation of 10 cm. Find the probability that the length of a randomly selected strip is: (a) Shorter than 165 cm. (b) Longer than 170 cm. (c) Between 145 cm and 155 cm.

### Set operations and Computations of Probabilities

Let P(A) denote the probability of a set A, and let A / B and A / B denote the union and intersection, respectively, of two sets A and B. If P(A) = 0.7, P(B) = 0.6, P(C) = 0.3, and P(A / C) = 0.2, find the minimum and maximum possible values of P(A / (B / C)).

### Questions of Algebra dealing with probability, etc.

1. True or False? 1.08 is a valid value for the correlation coefficient, r. 2. True or False? -0.835 is a valid value for the correlation coefficient, r. 3. Using the scatter plot below, determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables.

### Expected Profits

Suppose that next year the U.S. will be in one of the following economic conditions: Boom, Moderate Growth, Recession, or Depression. The probability that each economic condition will occur, and that a jewelry store will earn profits within that broader economic condition are listed below: Economic Condition Probability Jewel

### Poisson Distribution and Machines

The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of . = 3 per day (approximately Poisson in nature). The crew can service an average of µ = 8 machines per day, with a repair time distribution that resembles the exponential distribution. Please help me with the

### Statistics and Probability: Jukebox Scenario

On a Jukebox with 2000 songs, what is the probability that a single song will play during a 1 hour period, a 3 hour period, a 5 hour period, or a 12 hour period? How many times would a single song play during the periods described?

### Probability that both defective lights will be found

A box contains two defective Christmas tree lights that have been inadvertently mixed with eight non-defective lights. If the lights are selected one at a time without replacement and tested until both defective lights are found, what is the probability that both defective lights will be found after exactly three trials?

### Statistical Probability: Emergency Call Rates

1. Let sample mean = 70 and the sample variance = 36 and assume the data is normally distributed. Use ths information to answer the following: a. what is the median of this data set? b. find an interval that would contain 68% of all data values from the sample. c. find the x-value that corresponds to the 16th percentile d.

### probability that the sample mean will be greater than M=10 pound

At the end of the spring semester, the Dean of Students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of a mean=9 pounds with a standard deviation=6. The distribution of scores was approximately no

### Determining Probability - Bank Loans and Card Decks

A deck contains three drawers. Drawer 1 contains two gold coins. Drawer 2 contains one gold coin and on silver coin. Drawer 3 contains two silver coins. I randomly choose a drawer and then randomly choose a coin. If a silver coin is chosen, what is the probability that I chose drawer 3? A customer has approached a bank for a

### Probability

I need help with the following: Fluctuation in the prices of precious metals such as gold have been empirically shown to be well approximated by a normal distribution when observed over short interval of time. In May 1995, the daily price of gold (1 troy ounce) was believed to have a mean of \$383 and a standard deviation of \$

### Life Tables

What are life expectancy tables and why are they important for life insurance companies?

### Classical and Empirical Probability - Coin Tossing

1. Describe two main differences between classical and empirical probabilities. Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between 16 and 30. You do not need more than that. Put all of the coins in a small bag or container big enough to allow th