Question

Question 1:In the layout of a printed circuit board for an electronic product, there are 12 different locations that can accomodate chips. (a) If Five different types of chips are to be placed on the board, how many different layouts are possible? (b) What is the probability that five chips that are placed on the board are of the same type? Question 2: A Web ad can be designed from 4 different colors, 3 font types, 5 font sizes, 3 images, and 5 text phrases. A specific design is randomly generated by the Web server when you visit the site. Let A denote the event that the design color is red and let B denote the event that the font size is not the smallest one. Find P(A ∪ B0 ) and P(B|A). Question 3: A batch of 500 containers for frozen orange juice contains 10 defective containers. Three are selected randomly without replacement from the batch. (a) What is the probability that the second one is defective given that the third one is defective? (b) What is the probability that the third one is defective? (c) What is the probability that the first one is defective given that the other ones are not defective? Question 4: A player of a video game is confronted with a series of 4 opponents and an 80% probability of defeating each opponent. Assume that the results are independent (and that when the player is defeated by an opponent the game ends). (a) What is the probability that a player defeats all 4 opponents in a game? (b) If the game is played 4 times, what is the probability that the player defeats all 4 opponents at most twice. Question 5: A credit card contains 16 digits. It also contains a month and year of expiration. Suppose there are one million credit card holders with unique numbers. A hacker randomly selects a 16-digit credit card number. (a) What is the probability that it doesn’t belong to a real user? (b) Suppose a hacker has a 10% chance of correctly guessing the month 2 of the expiry and randomly selects a year from 2018 to 2025. What is the probability that the hacker correctly selects the month and year of expiration (all the years are equally likely)? Question 6: An optical inspection system is to distinguish among different parts. The probability of a correct classification of any part is 98%. Suppose that 3 parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified. (a) Determine the probability mass function X. (b) Find P(X ≤ 2)

Answer 1