If a component is selected randomly from a large batch, and that component is defective, find the probability that it was produced: (a) by M2, and (b) by M3.
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- Based on geological studies done in Alaska, a petroleum company believes the probability of finding high quality oil is 25%, medium quality oil is 41%, and no oil is 34%. Since drilling can be expensive, the petroleum company also plans on doing a soil test (since certain oil types are more apt to detect the presence and quality of oil). For example, the petroleum company knows that in 24% of high quality oil finds, 16% of medium quality oil finds, and 14% of no oil finds, the soil is Type A. So for Alaska... Find the probability that high quality oil is found given the soil was not Type A.When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 10% of the wells had neither impurity, 90% had impurity A, and 20% had impurity B. (Obviously, some had both impurities.) If a well is randomly chosen from those in the county, find the probability distribution for Y, the number of impurities found in the well. P(no impurities)= P(exactly one impurity)= P(both impurities)=A bakery sells three types of bread: sourdough, wheat, and rye. The sales data from the past month shows that 40% of the bread sold was sourdough, 30% was wheat, and 30% was rye. On a particular day, the bakery sold 100 loaves of bread. What is the probability that the bakery sold more than 50 loaves of sourdough bread?
- A gasoline manufacturer has two big projects worldwide, one is in Southeast Asia and the other one is along Africa. The probability of the project in Southeast Asia being successful is 40% and that of the project in Africa is 70%. Suppose that the success of the two projects are independent of each other, find the probability that only the Southeast Asian project succeed given that at least one of the two projects is successful. Select the correct response: 30% none of these 80% 45% 15%A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $1,425,000 if successful and a yearly loss of $475,000 otherwise. The probability of success is 1. If the second mall is selected, it is estimated that the yearly profit will be $950,000 if successful; 3 otherwise, the annual loss will be $285,000. The probability of success at the second mall is Complete parts (a) through (c) below 4 - a. What is the expected profit for the first mall?A manufacturing company is faced with the problems of choosing four products to manufacture. The potential demand for each product may turn out to be good, satisfactory, or poor. Probabilities for each type are given below: Products Probabilities Good Satisfactory Рoor A 0.60 0.20 0.20 В 0.75 0.15 0.10 C 0.60 0.25 0.15 D 0.50 0.20 0.30 The estimated profit/loss under different states of demand may be taken as under. uct Profit or Loss Good Satisfactory Poor A 40,000 10,000 1,100 40,000 20,000 |-7,000 C 50,000 15,000 |-8,000 D 40,000 18,000 15,000 Prepare expected value table and advice the company about the choice of the product.
- A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (22)%, and (13)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2?A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (20+I)%, and (10+H)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2? H is 3 and I is 2A retailer of automobile parts has four employees, K, L, M, and N, who make mistakes in filling an order one time in 100, four times in 100, two times in 100, and six times in 100. Of all the orders filled, K , L, M, and N fill, respectively, 20%, 40%, 30%, and 10%. If a mistake is found in a particular order, what are the probabilities that it was filled by K, L, M, or N?
- In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that: The health service will diagnose an adult over age 50 as having diabetes. A person over 50 diagnosed by the health service as having diabetes actually has the disease.A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.95, P(C) = 0.91, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to six decimal places.The accidents that occur in a manufacturing company were classified by severity (strong, moderate and mild) and by sex with the following characteristics: 40% of the accidents were strong and 30% were moderate. Women suffered 20% of the accidents. Of the total number of serious accidents, men suffered 85.5% of the accidents. Similarly, of the total moderate accidents, women suffered 45% of the accidents. Calculate the following probabilities:- If a woman suffered an accident, what is the probability that it was minor?- If a man suffered an accident, what is the probability that he is strong?
