Question

In Questions 2-4 suppose there are a total of 15 Carbon Monoxide Detectors in a building and event “Y” is defined as Y={At least 9 of these detectors work}. Further suppose P(each detector work)=0.8, and detectors are independent of each other. Which of the following is the Ybar (complement of Y)? A. Ybar={At least 5 detectors fail} B. Ybar={At least 6 detectors fail} C. Ybar={At most 6 detectors fail} D. Ybar={At least 7 detectors fail} E. Ybar={At most 7 detectors fail}

Question 3 of 10 What is the probability that detectors number 3, 4, 11, 15 fail and the other 11 detectors work? A. 0.8^4 * 0.2^11 * 15!/(4! * 11!) B. 0.8^4 * 0.2^11 C. 0.8^11 * 0.2^4 * 15!/(4! * 11!) D. 0.8^11 * 0.2^4

Question 4 of 10 What is the probability that 11 detectors work and 4 detectors fail? (Hint: Here we don’t care which 4 to fail, just any 4). A. 0.8^4 * 0.2^11 * 15!/(4! * 11!) B. 0.8^4 * 0.2^11 C. 0.8^11 * 0.2^4 * 15!/(4! * 11!) D. 0.8^11 * 0.2^4

Answer 1

Answer - 2: y bar = Complement of y = At least 7 detectors fail

Option D is correct.

Answer - 3: P(Detectors 3, 4, 11, 15 fails)

= 0.8^11 * 0.2^4

Option D is correct.

Answer - 4: P(Any four detector fails)

= 0.8^11 * 0.2^4 * 15!/(4! * 11!)

Option C is correct.