6) The following circuit operates only if there is a path of functional devices

Question

6) The following circuit operates only if there is a path of functional devices from left to right. The probability that each device functions is shown in the graphic. Assume that devices fail independently. What is the probability that the circuit operates? (10 points) 0.90 0.90 0.90- 0.95 0.98 0.90 H 7) Assume P(A) 0.45, P(B) 0.30, and PCAnB) 0.2 a) Draw the Venn diagram. (5 points) b) Find P(A' U B) (4 points) c) Find P(A' n B') (4 points) d) Find P(AU B)' (4 points) Assume there is a lot of 20 widgets. The probability of failure of the widget is 0.15. at least four failed widgets? (15 points) 8) What is the probability that the lot contains 9) Assume you are the quality inspector. You have 7 parts to inspect. The probability that the part will pass inspection is 0.75 Calculate the probability that exactly 3 parts will pass inspection. (10 points)

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6. The probability that the circuits :

Whatever is in series just multiply to get the probability that the circuit operates:
= .98*(1-(1-.90)^3)*(1-(1-.95)(1-.90))
= .9741

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