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 9 Resistance Low 16 15 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 8 Low conductivity 15 3 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