Problem #2: 12 students from each of Engineering, Science, Humanities, and Social Science were nominated to represent their faculties. 9 of these 48 students will be randomly chosen to be on the student council. Find the probability that at least one of the four faculties will be unrepresented on the student council. Enter your answer Problem #2: symbolically, as in these examples Just Save Submit Problem #2 for Grading Problem #2 Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Attempt #6 Attem Your Answer: Your Mark:Problem #5: A lot of 94 semiconductor chips contains 17 that are defective. (a) Two are selected, one at a time and without replacement from the lot. Determine the probability that the second one is defective. (b) Three are selected, one at a time and without replacement. Find the probability that the first one is defective and the third one is not defective. Problem #5(a): Round your answer to 4 decimals. Problem #5(b): Round your answer to 4 decimals.Problem #6: An email filter is planned to separate valid e-mails from spam. The word free occurs in 71% of the spam messages and only 3% of the valid messages. Also, 17% of the messages are spam. (a) If an email message is randomly selected, find the probability that it is spam, given that it contains the word free. (b) If an email message is randomly selected, find the probability that it is valid, given that it does not contain the word free. Problem #6(a): Answer correct to 4 decimals Problem #6(b): Answer correct to 4 decimalsProblem #8: Consider the system of independent components connected as in the figure below. The system works only if there is a path of functional components from left to right. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works. Since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. Suppose that P(1 works) = 0.73, P(2 works) = 0.72, P(3 works) = 0.87, and P(4 works) = 0.88, and these events are mutually independent. (a) Find the probability that the system works. (b) Find the probability that component 1 works, given that the system works. Problem #8(a): Round your answer to 4 decimals. Problem #8(b): Round your answer to 4 decimals