PROBABILITY in .NET

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CHAPTER 2 PROBABILITY
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device is as shown. What is the probability that the circuit operates
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0.01 0.01 0.1
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2-109. The probability of getting through by telephone to buy concert tickets is 0.92. For the same event, the probability of accessing the vendor s Web site is 0.95. Assume that these two ways to buy tickets are independent. What is the probability that someone who tries to buy tickets through the Internet and by phone will obtain tickets 2-110. The British government has stepped up its information campaign regarding foot and mouth disease by mailing brochures to farmers around the country. It is estimated that 99% of Scottish farmers who receive the brochure possess enough information to deal with an outbreak of the disease, but only 90% of those without the brochure can deal with an outbreak. After the rst three months of mailing, 95% of the farmers in Scotland received the informative brochure. Compute the probability that a randomly selected farmer will have enough information to deal effectively with an outbreak of the disease. 2-111. In an automated lling operation, the probability of an incorrect ll when the process is operated at a low speed is 0.001. When the process is operated at a high speed, the probability of an incorrect ll is 0.01. Assume that 30% of the containers are lled when the process is operated at a high speed and the remainder are lled when the process is operated at a low speed. (a) What is the probability of an incorrectly lled container (b) If an incorrectly lled container is found, what is the probability that it was lled during the high-speed operation 2-112. An encryption-decryption system consists of three elements: encode, transmit, and decode. A faulty encode occurs in 0.5% of the messages processed, transmission errors occur in 1% of the messages, and a decode error occurs in 0.1% of the messages. Assume the errors are independent. (a) What is the probability of a completely defect-free message (b) What is the probability of a message that has either an encode or a decode error 2-113. It is known that two defective copies of a commercial software program were erroneously sent to a shipping lot that has now a total of 75 copies of the program. A sample of copies will be selected from the lot without replacement. (a) If three copies of the software are inspected, determine the probability that exactly one of the defective copies will be found. (b) If three copies of the software are inspected, determine the probability that both defective copies will be found.
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(c) If 73 copies are inspected, determine the probability that both copies will be found. Hint: Work with the copies that remain in the lot. 2-114. A robotic insertion tool contains 10 primary components. The probability that any component fails during the warranty period is 0.01. Assume that the components fail independently and that the tool fails if any component fails. What is the probability that the tool fails during the warranty period 2-115. An e-mail message can travel through one of two server routes. The probability of transmission error in each of the servers and the proportion of messages that travel each route are shown in the following table. Assume that the servers are independent. probability of error percentage of messages server 1 server 2 server 3 server 4 route 1 30 0.01 0.015 route 2 70 0.02 0.003 (a) What is the probability that a message will arrive without error (b) If a message arrives in error, what is the probability it was sent through route 1 2-116. A machine tool is idle 15% of the time. You request immediate use of the tool on ve different occasions during the year. Assume that your requests represent independent events. (a) What is the probability that the tool is idle at the time of all of your requests (b) What is the probability that the machine is idle at the time of exactly four of your requests (c) What is the probability that the tool is idle at the time of at least three of your requests 2-117. A lot of 50 spacing washers contains 30 washers that are thicker than the target dimension. Suppose that three washers are selected at random, without replacement, from the lot. (a) What is the probability that all three washers are thicker than the target (b) What is the probability that the third washer selected is thicker than the target if the rst two washers selected are thinner than the target (c) What is the probability that the third washer selected is thicker than the target 2-118. Continuation of Exercise 2-117. Washers are selected from the lot at random, without replacement. (a) What is the minimum number of washers that need to be selected so that the probability that all the washers are thinner than the target is less than 0.10 (b) What is the minimum number of washers that need to be selected so that the probability that one or more washers are thicker than the target is at least 0.90
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