A computer intrusion detection system (IDS) is designed to provide an alarm whenever there is unauthorized access into a computer system. A probabilistic evaluation of a system with two independently operating intrusion detection systems (a double IDS) was published. Consider a double IDS with system A and B. If there is an intruder, A sounds an alarm with probability .9 and system B sounds an alarm with probability .95. If there is no intruder, the probability system A will sound an alarm is .2 and system B is .1a). if there is an intruder, what is the probability that both systems sound an alarm?b) given that there is an intruder, what is the probability that at least one of the systems sounds an alarm?

On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate.   b sketch a tree diagram to model this process

Students in a class like to secretly use online calculators in their quizzes. There are three such online calculators favoured amongst the students: WolframAlpha (WA), Symbolab (S), and GeoGebra (GG). A student's favourite calculator changes from quiz to quiz according to the following rules: If a student likes WA best, then it is has a 50% chance of remaining their favourite for the next quiz; 25% of becoming S for the next quiz; and 25% of becoming GG for the next quiz.  If a student likes S best, then it has a 50% chance of becoming WA for the next quiz, and a 50% chance of becoming GG for the next quiz.  If a student likes GG best, then it has a 33.3% chance of becoming any of the three calculators for the next quiz.  For the first quiz, there are 120 who count WA as their favourite; 80 who count S as their favourite; and 50 who count GG as their favourite.  What is true about the fourth quiz? Choose one of the following: 1. 115 students favour WA; 52 students favour S; and 83…

Suppose there is a 3-stage experiment that are pairwise independent (i.e. they’re all independent from eachother). If stage one has 5 outcomes stage two has 6 outcomes and stage three has 2 possible outcomes, howmany outcomes does the experiment itself have?

A planned community has 150 homes, each with an automatic garage door opener. The door opener has seven switches that a homeowner can set to 0 or 1. For example, a door opener code might be 1001100. Assuming all the homes in the community are sold, what is the probability that at least two homeowners will set their switches to the same code, and will therefore be able to open each other's garage doors?

A recent study sought to determine if exercising after studying for an exam may help retain information. The 150 student volunteers that participated in the study were randomly assigned to three groups. All students were given a picture memory task that they studied for 15 minutes. After studying, one of the groups was instructed to exercise for 30 minutes immediately after studying. A second group was instructed to wait 1 hour after studying and then exercise for 30 minutes. The third group was instructed to not exercise after studying. The next day all 150 student volunteers were given a test to determine how well they could remember what they studied. Here are the results:   The researchers want to test: H0: There is no difference in the distribution of performance on the test for the three treatment groups among the population of all student volunteers like these. Ha: There is a difference in the distribution of performance on the test for the three treatment groups among the…

A production line has three machines A, B, and C, with reliabilities of .90, .95, and .98, respectively. The machines are arranged so that if one breaks down, the others must shut down. Engineers are weighing two alternative designs for increasing the line's reliability. Plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. In either case, three machines (A, B, and C) would be used with reliabilities equal to the original three. a. Compute overall system reliability under Plan 1. (Round your intermediate calculations and final answer to 4 decimal places.) Reliability b. Compute overall system reliability under Plan 2. (Round your intermediate calculations and final answer to 4 decimal places.) Reliability c. Which plan will provide the higher reliability? Plan 1 O Plan 2