Human beings have 4 types of basic blood type: AB, A, B and O. In the US, about 43% of people are O type, 43% of people are A type, 10% of people are B type and 4% of people are AB type'. Now you are a doctor and have two patients waiting for blood transfusion. One of them has blood type O and can only accept blood type 0 transfusion; the other has blood type A and can receive either type O or A transfusion. Assume every donor's contribution can only support one patient (that is, one donor cannot donate blood to both patients). If you choose 5 donors randomly from the population, what's the probability that both of the patients are able to get blood transfusion? Round to four decimal places.
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- Explain the differences between Gaussian elimination and Gauss-Jordan elimination.Two bicycle manufacturers, Alpha Cycles (A) and Best Bikes (B), buy parts from the suppliers Firm Frames (F), Great Gears (G) and Happy Handlebars (H). During the year 2019: 50% of the frames from Firm Frames (F) were sold to Alpha Cycles (A) and 50% were sold to Best Bikes (B). 75% of the gear sets from Great Gears (G) were sold to Alpha Cycles (A) and 25% were sold to Best Bikes (B). 40% of the handlebars from Happy Handlebars (H) were sold to Alpha Cycles (A) and 60% were sold to Best Bikes (B). Draw a network diagram with input nodes F, G and H, and output nodes A and B, that represents the proportion of parts sold from each supplier to each bicycle manufacturer Write down the matrix that represents this network. Use the matrix that you found to determine how many parts were sold to Alpha Cycles (A) during 2019, if the total number of parts sold to the two bicycle manufacturers by Firm Frames (F), Great Gears (G) and Happy Handlebars (H) was 240, 320 and 300 parts respectively.The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. a. What is the probability that a part that passes quality control inspection was produced by Machine Y? Enter your answer in decimal form and round to four decimal places if rounding is necessary. Blank 1. Calculate the answer by read surrounding text.b. What is the probability that a part doesn't pass quality control inspection? Enter your answer in decimal form and round to four decimal places if rounding is…
- The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. a. What is the probability that a part that passes quality control inspection was produced by Machine Y? Enter your answer in decimal form and round to four decimal places if rounding is necessary.The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. d. What is the probability that a part is produced by Machine X and doesn't pass quality control inspection? Enter your answer in decimal form and round to four decimal places if rounding is necessary.The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. c. What is the probability that a part passes quality control inspection, given that it was produced by machine Z? Enter your answer in decimal form and round to four decimal places if rounding is necessary.
- The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. b. What is the probability that a part doesn't pass quality control inspection? Enter your answer in decimal form and round to four decimal places if rounding is necessary.The economy of a small country consists of three sectors: Energy, Manufacturing and Agriculture. For each $1 worth of output, the Energy sector requires $0.20 worth of input from the Energy sector, $0.20 worth of input from the Manufacturing sector and $0 worth of input from the Agriculture sector; the Manufacturing sector requires $0.40 worth of input from the Energy sector, $0.20 worth of input from the Manufacturing sector and $0.20 worth of input from the Agriculture sector; the Agriculture sector requires the same levels of input as the Manufacturing sector does. What level of output should each sector produce in order to meet a consumer demand of $3 million worth of Energy, $2 million worth of Manufacturing and $1 million worth of Agriculture? (Use Gauss-Jordan elimination for matrix inversion.)In a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation. (a) Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters. P A T = P A (b) Find the initial distribution vector for this Markov chain. X0 = (c) What percentage of the commuters are expected to use public transportation 6 months…
- A snowboard manufacturer has three plants, one in the eastern United States, one in the western United States, and one in Canada. Production records show that the U.S. plants each produced 10,000 snowboards last month, while the Canadian plant produced 8000 boards. Of all the boards manufactured in Canada last month, 4% had a defect that caused the boards to delaminate prematurely. Records kept at the U.S. plants show that 3% of the boards manufactured in the eastern United States and 6% of the boards manufactured in the western United States had this defect as well. a) What proportion of the boards manufactured last month were defective? b) What is the probability that a snowboard is defective and was manufactured in Canada? c) Given that a snowboard is defective, what is the probability that it was manufactured in the United States?The city of San Fransokyo is a high-tech city, especially in the field of robotics. There are three big companies that rule the city: Granville, Axcel, and Hamada. The Granville company controls about 50% of the total robot manufacturing in the city of San Fransokyo; Axcel company controls 35%; while the rest is controlled by the Hamadacompany. Based on the information you have obtained, it turns out that 3% of the robots made by Granville have problems with the sensing ability ofthe robot. As much as 5% robots made by Axcel and 1% robots made by Hamada also have the same problem. You want to buy a robot to help with your business and randomly pick up exactly one robot from the three companies. After the item arrives, you do a test, and it turns out that the robot is experiencing a malfunction in its sensing component. Using the Bayes Rule approach, which company is predicted to make the robot you bought? Justify your answer with adequate calculations!A can of cat food, guaranteed by the manufacturer to contain at least 10 units of protein, 20units of mineral matter, and 6 units of fat, consists of a mixture of four different ingredients.Ingredient A contains 10 units of protein, 2 units of mineral matter, and 1 2 unit of fat per100g. Ingredient B contains 1 unit of protein, 40 units of mineral matter, and 3 units of fat per100g. Ingredient C contains 1 unit of protein, 1 unit of mineral matter, and 6 units of fat per100g. Ingredient D contains 5 units of protein, 10 units of mineral matter, and 3 units of fatper 100g. The cost of each ingredient is 3c, 2c, 1c, and 4c per 100g, respectively. How manygrammes of each should be used to minimise the cost of the cat food, while still meeting theguaranteed composition?