Mat201 Week 1

Module 1 - Case

Introduction to Probability

ASSIGNMENT OVERVIEW

To complete this assignment, first review Chapter 3: Probability Topics from the background reading using the OpenStax e-textbook. Please have special focus on the following sections:

3.1 Terminology 3.2 Independent and Mutually Exclusive Events 3.3 Two Basic Rules of Probability 3.6 Probability Topics

Please note: By submitting this assignment, you affirm that it contains all original work, and that you are familiar with Trident University’s Academic Integrity policy in the Trident Policy Handbook. You affirm that you have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. You affirm that the assignment was completed individually, and all work presented is your own.

CASE ASSIGNMENT

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible. If the answer is in %, show two decimal places.

Answer the following problems showing your work and explaining (or analyzing) your results. Submit your work in a typed Microsoft Word document.

1. During an economic downturn, Lanier Company is forced to lay off employees. The table below breaks down the layoffs:

   	Being Laid Off	Not Being Laid Off	Total
   Managers	50	235	285
   Non-Managers	125	575	700
   Total	175	810	985

   1. What is the probability that an employee of Lanier is being laid off given that she/he is a non-manager? (3 pts)
   2. What is the probability that an employee selected at random is a manager? (3 pts)
2. The following data set represents the average day temperature in Orange County, Calif., for 20 days in December.

   Degrees (in Fahrenheit)
   43	65	55	49	60	52	45	61	59	47
   62	46	65	57	44	64	53	48	63	56

   Find the probability that a randomly selected day will have an average temperature of at least 60 ℉. (4 pts)
3. A survey was taken to determine the birthplace of a class of students in a statistics class. Below is the data set.

   Gender	Number of Students	Birthplace
   Male Female	6 10	San Diego San Diego
   Male Female	12 8	Los Angeles Los Angeles
   Male Female	5 9	San Francisco San Francisco

   1. What is the probability that a student was born in Los Angeles given the student was male? (3 pts)
   2. What is the probability a student was born in San Diego or the student was female? (3 pts)
4. What is the probability of throwing one die and getting a number greater than 5? (4pts)
5. Two coins are tossed 100 times. Below is the data set:

   Two heads	29
   One heads	45
   No heads	26

   1. What is the probability of getting two heads? (3 pts)
   2. What is the probability of getting no heads? (3 pts)
6. Broad Tire Manufacturing Company kept a record of the distance before a tire needed to be replaced. The table shows the results of 500 tires.

   Distance in miles	Less than 2,500	2,500–5,500	5,501–8,700	More than 8,700
   Frequency	10	105	160	225

   1. If a tire is bought from this company, what is the probability that it must be replaced with less than 2,500 miles? (3 pts)
   2. What is the probability that it will last more than 5,500 miles? (3 pts)
7. Two golfers, Phillips and Woodson, play a golf match. The probability of Phillips winning the match is 56%. What is the probability of Woodson winning the match? (4pts)
8. The percentage of grades obtained by a student in five tests is given below:

   Test	1	2	3	4	5
   % of Grades	65	80	73	79	59

   Find the probability of the student getting at least 70% on a test. (4 pts)
9. Find the probability of correctly answering the first 5 questions on a multiple- choice test by randomly guessing the answer. Each question has 4 possible answers. (4 pts)
10. One card is drawn from a deck of 52 cards, well-shuffled.
    1. Calculate the probability that the card will be an ace or a king. (3 pts)
    2. Calculate the probability the card will be a queen. (3pts)