Question 1:In the layout of a printed circuit board for anelectronic product, there are 12 different locations that canaccomodate chips. (a) If Five different types of chips are to beplaced on the board, how many different layouts are possible? (b)What is the probability that five chips that are placed on theboard are of the same type? Question 2: A Web ad can be designedfrom 4 different colors, 3 font types, 5 font sizes, 3 images, and5 text phrases. A specific design is randomly generated by the Webserver when you visit the site. Let A denote the event that thedesign color is red and let B denote the event that the font sizeis not the smallest one. Find P(A ? B0 ) and P(B|A). Question 3: Abatch of 500 containers for frozen orange juice contains 10defective containers. Three are selected randomly withoutreplacement from the batch. (a) What is the probability that thesecond one is defective given that the third one is defective? (b)What is the probability that the third one is defective? (c) Whatis the probability that the first one is defective given that theother ones are not defective? Question 4: A player of a video gameis confronted with a series of 4 opponents and an 80% probabilityof defeating each opponent. Assume that the results are independent(and that when the player is defeated by an opponent the gameends). (a) What is the probability that a player defeats all 4opponents in a game? (b) If the game is played 4 times, what is theprobability that the player defeats all 4 opponents at most twice.Question 5: A credit card contains 16 digits. It also contains amonth and year of expiration. Suppose there are one million creditcard holders with unique numbers. A hacker randomly selects a16-digit credit card number. (a) What is the probability that itdoesn’t belong to a real user? (b) Suppose a hacker has a 10%chance of correctly guessing the month 2 of the expiry and randomlyselects a year from 2018 to 2025. What is the probability that thehacker correctly selects the month and year of expiration (all theyears are equally likely)? Question 6: An optical inspection systemis to distinguish among different parts. The probability of acorrect classification of any part is 98%. Suppose that 3 parts areinspected and that the classifications are independent. Let therandom variable X denote the number of parts that are correctlyclassified. (a) Determine the probability mass function X. (b) FindP(X ? 2)