STAT 3115 – Homework #2
Due Date: Friday February 5th, Beginning of Class
Note: Please include the following information on the first page of your completed homework.
1. Your name
2. STAT 3115 – LEC 1D
3. Homework #2
4. Due Date
5. List of students you worked with on this assignment (if applicable)
Guidelines: Please remember to show your work and explain your answers as necessary. Answers that are not supported by reasoning will not receive full credit. Homework should be stapled if it is longer than one page. Numbered problems are from Devore, 8th ed. unless otherwise noted.
Section 2.1 Problems:
1- #2 – In addition to parts (a-e) also list out all outcomes in the sample space (S)
2- #8 (a-d)
3- Resistors. An electrical engineer has two boxes containing different types of resistors. The first box contains 3 resistors of one type and the second box contains 2 resistors of another type. The engineer needs to test all of the resistors to see if they are acceptable for a certain task. Let (a,b) represent the event that the engineer will find a acceptable resistors in the first box and b acceptable resistors in the second box. Answer the following: a) List all possible outcomes in the sample space. b) List all outcomes in the event C, the event that none of the resistors in the first box are acceptable. c) List all outcomes in the event D, the event that fewer resistors in the first box than the second box are found acceptable. d) List all outcomes in C?D. e) List all outcomes in ‘CDn.
Section 2.2 Problems:
4- #12
5- # 13
6- Blood Types. Human blood may contain either or both of two antigens, A and B. Blood that contains only the A antigen is type A, blood that contains only the B antigen is type B, blood that contains both antigens is type AB, and blood that contains neither is type O. At a certain blood bank, 35% of the blood donors have type A, 10% have type B, and 5% have type AB. Answer the following: a) What is the probability that a randomly chosen donor is type O? b) A recipient with type A blood may safely receive blood from a donor whose blood does not contain the B antigen. What is the probability that a randomly selected donor may donate to a recipient with type A blood?
7- Aircraft Defects. Hydraulic landing assemblies coming from an aircraft rework facility inspected for defects. Historical records indicate that 8% have defects in shafts only, 6% have defects in bushings only, and 16% have at least one of the two types of defects. One of the assemblies is selected at random. What is the probability that it: a) Has both types of defects? b) Has a bushing defect? c) Has exactly one of the two types of defects? d) Has neither type of defect?
8- Employee Opinions. The table below classifies employees at a certain company with respect to their gender and their sentiment (Favor, Neutral, Opposed) to a new software that is being considered for adoption.
Favor
Neutral
Opposed
Male
80
20
50
Female
40
10
50
Suppose one of the employees is randomly selected.
a. What is the probability of selecting a female employee?
b. What is the probability of selecting an employee that is not opposed to the new software?
c. What is the probability of selecting an employee that is female and opposed to the new software?
d. What is the probability of selecting an employee that is female or opposed to the new software?
9- Gene Expression. In studies of the human genome, gene expression levels are often studied to investigate patterns that might identify certain diseases. Consider three different genes A, B, and C that have the potential to cause cancer (called oncogenes). In a sample of cancer patients it was found that:
• 60% have high expression of gene A, 40% have high expression of gene B, and 25% have high expression of gene C.
• 70% have high expression of A or B (or both), 69% have high expression of A or C (or both), and 52% have high expression of both B or C (or both)
• 8% have high expression of all three genes.
Find the probability that a randomly selected cancer patient.
a. Does not have high expression in gene A.
b. Has high expression in both genes A and B.
c. Has high expression in both genes A and B, but not C.
d. Has high expression in at most two genes.