1. (5 points) Provide a reasonable description of the sample space for this scenario: The voids in a ferrite slab are classified as small, medium, or large. The number of voids in each category is measured by an optical inspection of a sample. 2. (5 points) Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized here: Shock Resistance High Low Scratch High 70 19 Resistance Low 16 Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch resistance. Determine the number of disks in A n B, A', and A U B.3. (5 points} In the design of an electromechanical product, 12 components are to be stacked into a cylindrical casing in a manner that minimizes the impact of shocks. One end of the casing is designated as the bottom and the other end is the top. If 3 components are of one type and identical to one another, and 4 components are of another type and identical to one another, but the others are different, how many different designs are possible? 4. (5 points} A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly, what is the probability that it is a valid number? 5. (5 points) Strands of copper wire from a manufacturer are analyzed for strength and conductivity. The results from 100 strands are as follows: Strength High Low High conductivity| 74 18 ow conductivity | 15 If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high? 6. (5 points) A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letters (a-z) or 26 uppercase letters (A-Z) or 10 integers (0- 9). Let Q denote the set of all possible passwords. Suppose that all passwords in Q are equally likely. Determine the probability that the password contains only even numbers given that it contains all numbers.(5 points} A lot of 100 semiconductor chips contains 20 that are defective. a. Two are selected, at random, without replacement, from the lot. Determine the probability that the second chip selected is defective. In. Three are selected, at random, without replacement, from the lot. Determine the probability that all are defective. (5 points} If PM} = 0.2, PlB) = 0.2, and A and B are mutually exclusive, are they independent? 9. (5 points} Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is found that 1% of the legitimate users originate calls from two or more metropolitan areas in a single day. However, 30% of fraudulent users originate calls from two or more metropolitan areas in a single day. The proportion of fraudulent users is 0.01%. If the same user originates calls from two or more metropolitan areas in a single day, what is the probability that the user is fraudulent? 10. (5 points} Decide whether a discrete or continuous random variable is the best model for each of the following variables: a. The time until a Wm earth. b. The number of times a transistor in a computer memory changes state in one operation. c. The volume of gasoline that is lost to evaporation during the lling of a gas tank. d. The outside diameter of a machined shaft