Homework #3 STAT351.001 Spring 2024 Due: Monday, April 29th Include all work in a neat and well organized presentation. Grading is based on the quality, thoroughness, and correctness of the work provided. You do not need to print out this assignment; you may provide your work and answers on your own separate paper (had written is sufficient). Upload your solutions as a single PDF file to the "Homework 3" submission folder in our Canvas course. Your submission should be titled "(your name) STAT351 Homework 3." Notes: 1. Show all work, points are awarded based on the work provided. 2. When providing probabilities provide them as numbers between 0 and 1 (not as percentages), and keep at least 3 decimal places. 1. A transmitted "message" consists of 10 bits". Each bit is decoded correctly with probability .999, independent of the decoding of all other bits. a. what is the probability that the entire message (all 10 bits) is decoded correctly? what is the probability that exactly one of the 10 bits is decoded incorrectly? b. C. what is the probability that two or more of the bits" is decoded incorrectly? 3. Computer keyboard failure can be attributed to either electrical defects or mechanical defects. A repair facility currently has 20 failed keyboards, 6 of which failed due to an electrical defect and the remaining 14 failed due to a mechanical defect (and none of the keyboards have both, electrical and mechanical, defects). Five of the 20 failed keyboards will be randomly selected. Determine each of the following probabilities: a. Find the probability that exactly 2 of the 5 keyboards have an electrical problem. Find the probability that at least one of each type of defect is selected? b. 4. 5. A system is composed of a number of identical components, each one of which is operational with probability 0.90, independent of the other components. Components function or fail independent of the performance of all other components. The system is operational if there is at least one functional path from A to B. What is the probability of this happening? A B A, B, and C are independent events where P(A) = P(B) = P(C) = 0.30. Are events A and B mutually exclusive? Explain (with numbers). Determine P(A|B). a. b. C. d. Determine P(A|AUC). Determine P((An B)|(ANC)).