**Module 1 – Case**

**Introduction to Probability**

**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.

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

2. | Being Laid Off | Not Being Laid Off | Total |

Managers | 50 | 235 | 285 |

Non-Managers | 125 | 575 | 700 |

Total | 175 | 810 | 985 |

- What is the probability that an employee of Lanier is being laid off given that she/he is a non-manager? (3 pts)
- What is the probability that an employee selected at random is a manager? (3 pts)
- 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 | 54 | 53 | 48 | 63 | 56 |

- Find the probability that a randomly selected day will have an average temperature of at least 60 ℉. (4 pts)
- 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 |

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

Two heads | 29 |

One heads | 45 |

No heads | 26 |

- What is the probability of getting two heads? (3 pts)
- What is the probability of getting no heads? (3 pts)
- 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 |

- 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)
- What is the probability that it will last more than 5,500 miles? (3 pts)
- 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)
- 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)
- 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)
- One card is drawn from a deck of 52 cards, well-shuffled.
- Calculate the probability that the card will be an ace or a king. (3 pts)
- Calculate the probability the card will be a queen. (3pts)