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In this assignment you will have an opportunity to practice probability calculations, including basic probabilities, Bayes’ Theorem, and expected value of empirical probability distributions.
Completing this assignment, will give you an opportunity to
Working is individually is recommended, but working in pairs may be helpful.
Prior to working on this assignment, it is suggest that you review these lessons and refer to them during the assignment:
A data set contains a list of 800 hockey players and the countries in which they were born. There are 11 unique countries, including Canada, Russia, Germany, USA, Sweden, Switzerland, among others. Assuming no other knowledge, what is the probability that a player chosen at random is from Germany?
A data set contains a list of 800 hockey players and the countries in which they were born. 387 players were born in Canada, 223 were born in the USA, 8 were born in Germany, 73 are from Russia, 81 from Sweden, 19 from Finland, 2 from Norway, 4 from Switzerland, 2 from France, and 1 from Austria.
Consider the data set CerealData.CSV.
SecSoft, LLC has developed a biometric airport security device that has a 92.6% chance of alerting authorities when a known and dangerous person-of-interest (POI) walks through the device. But, when a “normal” traveler walks through there’s a 6.5% chance that it incorrectly flags the traveler as a POI. Some research has shown that in a typical airport setting, 1 in 11,000 is a POI. If a traveler sets of the alarm what is the probability that the person is actually a person of interest?
A factory has two assembly lines that produce USB drives. Line 1 produces 68% of the total drives, and Line 2 produces 32%. Past records show that Line 1 produces a defective drive 1% of the time, while Line 2 produces a defective widget 2% of the time.
A USB drive is chosen at random from the day’s entire production and it is found to be defective. What is the probability that the defective widget was produced on Line 1?
A new test (Cologuard) for the screening for colon cancer was recently approved. The manufacturer of the test says the following: “13% of people without cancer received a positive result (false positive) and 8% of people with cancer received a negative result (false negative)”.
If you receive a negative result from the test, what is the probability you actually do have color cancer? You will need to find additional probabilities through your own research, e.g., P(C), the overall incidence rate of colon cancer in their target population of 50+ adults.
What if you cannot find an empirical estimate for a needed probability?
Consider a small coffee shop that sells four types of coffee: Espresso, Cappuccino, Latte, and Americano. The shop has kept track of the number of each type of coffee sold over the past week, and the data is as follows:
Espresso: 180 cups Cappuccino: 150 cups Latte: 230 cups Americano: 140 cups
Create an empirical probability distribution for the types of coffee sold at the shop.
Assume that an espresso costs 1.50, a cappucino 2.75, a latte 3.00, and an americano 2.20, calculate the average revenue for a coffee.
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