1. Patients are known to arrive at a pharmacy randomly, with an average rate of four patients arriving per hour

1.1 What is a probability that exactly three patients will arrive at the pharmacy during a particular hour

1.2 What is the probability that only one patient will arrive at the pharmacy during a 30 minutes interval

1.3 What is the probability that seven patient will arrive at the pharmacy during a two hour interval

2. An aeroscape compagny has submitted bids on two separate government contracts A and B. the compagny feels that it has 50% chance of winning contract A and 40% chance of winning contract B. Futhermore, it belives that winning contract A is independent of winning contract B.

2.1 What is the probability that the compagny will win both contracts?

2.2 What is the probability that the compagny will win at least one of the contracts?

3. A compagny has two vacancies at the junior executive level. Ten people, consisting of seven men and three women, are eligible and equally qualified. The compagny has decided to draw two names at random from the list of those eligible.

3.1 What is the probability that both positions will be filled by women?

3.2 What is the probability that at least one of the positions will be filled by a woman?

3.3 What is the probability that both positions will be filled by a man?

3.4 From your answers, what conclusions can be reached about the vacancies?

When testing for a disease such as the flu, there is always the possibility of receiving a false negative (meaning that you have the disease but tested negative) and a false positive (meaning that you do not have the disease but tested positive).

Last month, a collection of people at a clinic were tested for the flu. After the results were confirmed after medication, here were the results.

1. 1) How many people were used in this study?

2. 2) What is the probability that someone at this clinic tested positive for the flu and actually had the flu?

3. 3) What is the probability that someone at this clinic tested negative for the flu and actually did not have the flu?

4. 4) What is the probability that someone tested at this clinic got a test result that was correct?

5. 5) What is the probability that someone tested at this clinic got an incorrect test result?

6. 6) What is the probability that a false positive was obtained? (Hint: This is the probability that someone tested positive, given that they actually did not have the flu).

7. 7) What is the probability that a false negative was obtained? (Hint: This is the probability that someone tested negative, given that they actually did have the flu).

8. 8) Looking at the rates in #5, 6, and 7, do you feel that this clinic’s error rate is too high? Support your answer with your thinking on this. (An answer of ‘yes’ or ‘no’ only will notreceive credit).

I have done the part(a) and the code is below.

For the part(b),

If the user has earned absolutely 0 amount of prize money, tell user which number would have given them the highest prize money:

e.g. "You are unlucky! If you guessed X, you would have won the most money!"

Otherwise, if the prize money is non-zero, after telling user the prize money he/she earned, print out the list of numbers that would have caused the player to have 0 prize money.

e.g. "You are so lucky! You could have 0 money if you have guessed …."

using System;

using System.Collections.Generic;

class GuessingGame{

    public static void Main(){

        Dictionary<int, int> prizes = new Dictionary<int, int>();

        Random rndGen = new Random(0);

        int num, money;

        int i=0;

        while(i<10){

            num = rndGen.Next(1, 20);

            money = rndGen.Next(1, 10000);

            if(!prizes.ContainsKey(num)){

                prizes.Add(num, money);

                i++;

            }

        }

        Console.Write("Enter two numbers(space separated): ");

        string[] line = Console.ReadLine().Split(' ');

        int num1 = Int32.Parse(line[0]);

        int num2 = Int32.Parse(line[1]);

        if(num1==num2 || num1<1 || num1>20 || num2<0 || num2>20)

            Console.WriteLine("quit");

        else{

            int prizeMoney = 0;

            if(prizes.ContainsKey(num1))

                prizeMoney += prizes[num1];

            if(prizes.ContainsKey(num2))

                prizeMoney += prizes[num2];

            Console.WriteLine("You earned {0} in total!", prizeMoney);

        }

    }

}

Will Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with the mean of 2 customers every 5 minutes. Assume that a Poisson probability distribution can be used to describe the arrival process.

a. Compute the probability that exactly 1 customer will arrive in a 5-minute period

b. Compute the probability that exactly 3 customers will arrive in a 5-minute period

c. Compute the probability that 2 or fewer customers will arrive in a 5-minute period

d. Delays are expected if more than 3 customers arrive during any a 5-minute period. What is the probability that delays will occur?

A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.131. Consider your next 32 purchases that produce a game piece. Calculate the following: This is a binomial distribution. Round your answers to at least 4 decimal places.

a) What is the probability that you win 5 prizes? 0.175 Incorrect

b) What is the probability that you win more than 6 prizes? 0.00177 Incorrect

c) What is the probability that you win between 2 and 5 (inclusive) prizes?

d) What is the probability that you win 3 prizes or fewer?

In a ternary (three level) communications system, 3 is transmitted three times more frequently than a 1 while a 2 is transmitted two times more frequently than 1.

Probability of receiving a 2 when is 1 transmitted is α/2 (same for receiving a 3).

Probability of receiving a 1 when 2 is transmitted is β/2 (same for receiving a 3).

The probability of receiving a 2 when 3 is transmitted is γ/2 (same for receiving a 1).

(a) Draw the transition or the structure of the channel indicating the various probabilities

(b) At the receiver a '1' is observed. Using part (a) or directly, estimate the probability that the observed 1 was transmitted as a 1?

(c) Using parts (a), (b), or directly, what is the probability of receiving a 2' or a ‘3'?

3. Probability+ Central Limit Theorem questions:

a. The return on investment is normally distributed with a mean of 10% and a standard deviation of 5%. What is the probability of losing money?

b. An average male drinks 2 liter of water when active outdoor (with a standard deviation of 0.7). An organization is planning for a full day outdoor for 50 men and will bring 110 liter of water. What is the probability that the organization will run out of water? (8)

c. The lifetime of a certain battery is normally distributed with a mean of 10 hours and standard deviation of 1 hour. There are 4 such batteries in the package.

i. What is the probability that the lifetime of all 4 batteries exceed 11 hours?

ii. What is the probability that the total lifetime of all 4 batteries will exceed 44 hours.

If a citizen of Ireland is selected at random, the probability they have red hair is 0.11. If several citizens are selected, assume it is done one at a time with replacement and consecutive selections are independent of each other. n=6 citizens will be randomly selected.

14a) What is the probability all six citizens will have red hair?

14b) What is the probability at least one will have red hair?

14c) What is the probability the first four randomly selected citizens will have red hair and the last two will not?

14d) What is the probability exactly 4 of the 6 citizens will have red hair? Hints:
What is the difference between this question and the last one? How many different ways can 4 “reds” and 2 “not-reds” be ordered?

Based on recent statistics, the probability that a smoker who lives in a rural area will die from lung cancer is 0.00065. The probability that a smoker from an urban area will die from lung cancer is 0.00085. The probability that a nonsmoker from an urban area will die from lung cancer is 0.00015, whereas the probability that a rural nonsmoker will die from lung cancer is 0.00001. Approximately 70 percent of the population live in urban areas, and about 30 percent live in rural areas. Assume that 20 percent of urban dwellers are smokers and that 10 percent of rural d0wellers are smokers.

Given only the information that a person died from lung cancer, what is the probability that this person was an urban dweller?

Question 8 options:

1) The average weight of a certain machined part is 475 grams, with a standard deviation of 5 grams.

a) What is the probability that a randomly selected part from the manufacturing line weighs less than 477 grams?

b) What is the probability that a randomly selected part from the manufacturing line weighs less than 472 grams?

c) What is the probability that a randomly selected part from the manufacturing line weighs at least 482 grams?

d) What is the probability that a randomly selected part from the manufacturing line weighs between 472 grams and 477 grams?

e) What is the probability that a randomly selected part from the manufacturing line weighs less than 472 grams or more than 477 grams?