You are given the following system that consists of one controller and three peripherals (P1, P2, and P3): P1 P2 Controller P2 P3 P1 P3 By inspection, it turns out that this system is up if the controller and at least 2 of the peripherals are functioning. The controller fails with a probability of p and any peripheral fails with a probability of a. All events are independent. If p=1/3 and a=1/2, what is the probability that the system is up?

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Select one:
O 1/9
O 1/3
O 1/4
O 1/2
O 1/6
Transcribed Image Text:Select one: O 1/9 O 1/3 O 1/4 O 1/2 O 1/6
You are given the following system that consists of one controller and three peripherals (P1, P2,
and P3):
P1
P2
Controller
P2
P3
P1
P3
By inspection, it turns out that this system is up if the controller and at least 2 of the peripherals
are functioning. The controller fails with a probability of p and any peripheral fails with a
probability of a. All events are independent.
If p=1/3 and a=1/2, what is the probability that the system is up?
Transcribed Image Text:You are given the following system that consists of one controller and three peripherals (P1, P2, and P3): P1 P2 Controller P2 P3 P1 P3 By inspection, it turns out that this system is up if the controller and at least 2 of the peripherals are functioning. The controller fails with a probability of p and any peripheral fails with a probability of a. All events are independent. If p=1/3 and a=1/2, what is the probability that the system is up?
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