Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrowideas from gpt, but please do not believe its answer.Very very grateful! 3.Suppose there are n audiences for a show, say X₁,..., Xn. Each audiencegets a switch which can be turned on or off. The switches are wired to m challenges ofthe form X₂ V X¡ V¬Xk (3-CNF, that is or of the variables / the negation of exactly 3variables). Leaving Blank would result in 20% for each part.(a)Suppose all audiences turn their respective switch on/off independentlyat random. Calculate the expected number of challenges being satisfied.(b)Suppose m→∞. Show that with (1)-probability, a random configu-ration of switches satisfy at least 75% of the challenges.

To calculate the expected number of challenges being satisfied,It consider each challenge…

Answered: 3. Suppose there are n audiences for a…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.CT: Chapter Test

Problem 5CT: A commuter must travel from Ajax to Barrie and back every day. Four roads join the two cities. The...

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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow
ideas from gpt, but please do not believe its answer.Very very grateful!

3.
Suppose there are n audiences for a show, say X₁,..., Xn. Each audience
gets a switch which can be turned on or off. The switches are wired to m challenges of
the form X₂ V X¡ V¬Xk (3-CNF, that is or of the variables / the negation of exactly 3
variables). Leaving Blank would result in 20% for each part.
(a)
Suppose all audiences turn their respective switch on/off independently
at random. Calculate the expected number of challenges being satisfied.
(b)
Suppose m→∞. Show that with (1)-probability, a random configu-
ration of switches satisfy at least 75% of the challenges.

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