Week 6 – Assignment: Calculate ProbabilitiesInstructionsFor this task, write a paper using the following structure: Begin with a one or two-paragraph introduction that summarizes the meaning of the reading material.
Answer all of the questions included in Parts 1 and 2 below. Be sure to answer questions using complete sentences and show all work in your calculations.
Provide a written conclusion, when appropriate
Include an essay section in your paper, which is described in Part 3 below.
Use the last part of your paper to include a paragraph or two that explains the information that you learned in the assignment. Explain all answers thoroughly. Support your paper with at least two references.
Part 1A basketball player shoots six free throws during a game. Give the sample space S for counting the number of free throws made.
In the popular American game of roulette, the roulette wheel has 38 spaces that are numbered 0, 00, and 1 through 36, 0.
Find the probability of getting the following:
a) A number that is less than 15, not counting 0 and 00;
b) A number that is a multiple of 3 or 5, not counting 0 and 00;
c) An odd number that is less than 15, not counting 0 and 00;
d) A number that is between 1 and 12, inclusive.
Playing cards are used in many popular card games such as poker and black jack. An image of a complete deck of cards is available at the website: Playing Card Frequencies (located under your weekly resources). Problems 4 and 5 are based on this set.Suppose that a card is randomly selected from an ordinary deck of cards. Find the probability of getting:
a) A card that is between 4 and 8, inclusive.
b) A card that is between 4 and 8, inclusive, or a club.
c) A card that is red, or is a queen.
d) A card that is not red and not a queen.
Two cards are chosen at random and without replacement from an ordinary deck of cards. What is the probability that they are both hearts?
When three dice are rolled find the probability of getting a sum of 7.
Suppose that you live in a city where the most popular car colors are as follows in terms of probabilities.
Color White Black Silver Gray Red Beige Blue Yellow Probability 0.25 0.19 0.16 0.10 0.09 0.08 0.06 0.02 a) Suppose that you were asked to choose a new car from this city at random and record its color. What is the probability that the vehicle you choose has a color not listed in the above colors?
b) What is the probability that the vehicle you choose is neither white nor is it black?
c) What is the probability that the vehicle you choose is either: Red, White or Blue?
d) If you were a car dealer and you had to order 50 new cars, would the color probabilities effect your decision of what colors to order?A fair die is tossed three times in a row. What is the probability that three sixes occur?
A certain lottery game has a probability of winning of 0.03 on any one game. Plays of this game are assumed to be independent. If you play this lottery four times, find the probability that you will win:
a) None of the four times.
b) Exactly one of the four times.
A broker at Goldman Sachs must decide among a computer stock and a beverage stock for a clients portfolio. There exist 5 possible computer stocks, and the probability of each being chosen is 1/5. There are four possible beverage stocks and the probability of each being chosen is 1/4.
a) Is the choice of the computer stock independent of the choice of a beverage stock? Explain why or why not.
b) Suppose that the broker decides that the computer stock is IBM and the beverage stocks is Coke-a-cola. Assuming these are independent, what is the probability the broker picks these two stocks?
Part 2Suppose that a shipment of 250 netbooks contained three defects, and 247 good units. Find the probability that when a company buys three units from this sample, they will receive:
a) There are three good units.
b) All three units will be defective.
c) There will be at least one unit that is good.
At a ceremony at a naval flight school, there were 18 Marines, 10 members of the Navy and three members of the Coast Guard who were given their wings. If we were to select three pilots at random to feature in an advertisement, find the probability that there will be:
a) One member from each of the four branches of the service.
b) Exactly three Marines out of the three chosen.
Suppose that 22 percent of United States households have a 3D television. Choose five households at random. What is the probability that at least one has a 3D television?
Suppose that the distribution of adjusted gross income reported on income taxes in a recent year is given below (in thousands of dollars):
Income < 15 15-29 30-99 100-199 200 Probability 0.283 0.234 0.348 0.103 0.032 a) What is the probability that a randomly chosen return shows an adjusted gross income of $30,000 or more? b) Given that a person shows an income of at least $30,000, determine the probability that the persons income $100,000 or more? An automobile company has 6,500 dealers who are polled to find out their annual incomes as well as their age. The number of dealers in each category are given below: Incomes (dollars) Dealers under 40 Dealers 40 and above TotalUnder 100,000 1,500 1,500 3,000100,000 and over 1,000 2,500 3,500Total 2,500 4,000 6,500 What is the probability that a randomly chosen dealer will: a) Have an income under $100,000? b) Will have an income under $100,000, given that he or she is under 40? c) Be age 40 and above, given they have an income of $100,000 and over? Company X retains a psychologist to assess whether job applicants are a good match for working on an assembly-line. The psychologist classifies applicants as one of A (good match), B (marginal), or C (bad match). Company X is also concerned about the event D, which occurs when an employee leaves the company within a year of being hired. Data on all people hired in the past five years give the probabilities below: P(A) = 0.5 P(B) = 0.45 P(C) = 0.3 P(A and B) = 0.2 P(B and C) = 0.15 P(A and C) = 0.2 P(A, B and C) = 0.1 P(A and D) = 0.1 P(B and D) = 0.1 P(C and D) = 0.2a) Use the Insert Shapes tools in Word to sketch a Venn diagram of the events A, B, and C. Place the appropriate probability in each of the eight regions. There are also some applicants that end up unclassified. b) What is the probability that an employee leaves within a year? Length: 5- 7 pages References: Include a minimum of two scholarly peer-reviewed resources.Upload your document and click the Submit to Dropbox button.Due Date Dec 16, 2018 11:59 PM External Resource (S): Books and Resources for this Week 1. Statistics in Practice Moore, D.S., Notz, W.I., & Fligner, M.A. (2015). Statistics in practice. New York, NY: W.H. Freeman. Read Chapters 11 and 122. Milefoot.com. (n.d.). Playing card frequencies. http://www.milefoot.com/math/discrete/counting/cardfreq.htm3. BUS-7200_Grading_Rubrics Supplemental (External) Resource
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