1) A certain delivery system offers both express and standard delivery. Seventy-

Question

1) A certain delivery system offers both express and standard delivery. Seventy-five percent of parcels are sent by standard delivery and 25% are sent by express. Of those sent standard, 80% arrive the next day, and of those sent express, 95% arrive the next day. Let A denote the event that the parcel was shipped express. Let B denote the event that the parcel arrived the next day. a) Construct the tree diagram for this scenario. (5 points) b) What is the probability that a randomly selected parcel was shipped express and arrived the next day? (5 points) c) What is the probability that a randomly selected parcel arrived the next day? (5 points) 2) 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 0.95 0.98 0.90 0.90 H 0.90

Explanation / Answer

2

For each part of this loop, the probability that it functions is 1 minus the probability that both
elements fail

so for all 0.90

the probability for the first loop is

1 - (1-0.9)^3 = 0.999

the probability for the second loop is

1 - (1-0.9)*(1-0.95) = 0.995  

now the probability that the circuit operates is

0.98 *0.999*0.995 = 0.974

we can answer only 1 question at a time , as per the answering guidelines

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