A company buys microchips from three suppliers-I, II, of providing microchips that contain 10% defectives; Su 5%; and Supplier III has a defective rate of 2%. Suppose current supply came from Suppliers I, II, and III, respect at random from this supply, what is the probability that i
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- A machine can be in one of four states: ‘running smoothly’ (state 1), ‘running but needs adjustment’ (state 2), ‘temporarily broken’ (state 3), and ‘destroyed’ (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine to…3. Light bulbs are made by three independent factories. The 1st plant delivered N1 = 30% of bulbs, the 2nd - N2 = 55% of bulbs, the 3rd - N3 = 15% of bulbs. The probability of manufacturing defect product at the first plant is P1 = 0.01, at the second - P2 = 0.015, at the third - P3 = 0.02. The store receives bulbs from all three factories. A random bulb is picked up for control and turns out to be defective. What is probability that it was produced by 2nd factory?17. A firm plans to bid Rs. 300 per kg. for a contract to supply 1,000 kg. ofa metal. It has two competitors A and B and it assumes that the probability that A will bid less than Rs. 300 per kg. is 0.3 and that B will bid less than Rs. 300 per kg. is 0.7, If the lowest bidder gets all the business and the firms bid independently, what is the expected value of the contract to the firm? n3 aer all All
- There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack, and you must pick one to protect. Suppose that the attacker is going to attack site i with probability q;. You plan on selecting a site to protect, with probability pi of selecting site i. The choice of {qi} and {p;} represent the attacker's and defender's strategy, respectively.5. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 2 using the Kaplan-Meir approach and interpret the results. Time in Years Number at Risk, Nt Number of Deaths, Dt Number Censored, Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85. The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study. The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment. The probability of surviving 2 years after…Suppose that a new detection tool is introduced starting in week 3 and that from week 3 onwards, each fake bill has a 1 in 3 chance of being detected at each transaction. In this case, what is the totalexpected number of times that the fake bills are successfully used in transactions without being detected?
- 1.A family wishes to adopt 4 pets from a total of 13 dogs and 7 cats available at an animal shelter. The variable "x" being measured is the number of dogs. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations using C(Dt). 2. A student forum at a high school needs to elect 5 people from 10 Grade 11 students and 15 Grade 12 students who are available. The variable"" being measured is the number of Grade 12 students. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations involving C(Dt).5. Two processes A and B, were used to produce stainless steel shafts in an industrial company. Process A and Process B produce 9% and 12% nonconforming stainless steel shafts, respectively. a. A random sample of 100 stainless steel shafts were taken from Process A. What is the UTM probability that more than 95% of the stainless steel shafts are conforming? b. A random sample of 90 stainless steel shafts from Process A and 80 stainless steel shafts UTM UT UTM 8U from Process B were taken randomly. Find the probability that the difference between proportion of the nonconforming stainless steel shafts from Process A and Process B UTM UTM is at most 0.1. O UTM UT UTM 6 UTM U O UTM UT