A factory has a machine shop in which three machines (A, B and C) produce 100cm aluminum tubesAn inspector is equally likely to sample tubes from A and B, and three times as likely to select tubes from C as he is from BThe defective rates from the three machines are: A: 10%B: 10%C: 20%What is the probability that a tube selected by the inspector:(i)is from machine A;(ii)is defective;(iii)comes from machine A, given that it is defective.
Put the ice cube in hot salt waterAnd then put the ice cube in extremely cold water, and that should keep it from melting for a whileHope I helped!
What are the constraints?To melt it faster.put mirrors around it Or a magnifying glass over it (will really only work outsideto slow the melting, I guess put a white box around it.This will reflect light away from it.keep it enclosed, the ice will cool the air in the box.will melt slower If you really don't want it to melt for a while.put a bunch of dry ice in there with the ice cube.
Put salt on one ice cubeThat will make it melt, but it will also lower the temperatureSeperate the two with some sort of sheet, like saran wrap and the cold temperature of the first should help the second stay colder longerThat's the first idea that came to my head, but i'm not sure how practical it would be for your class.
Making it melt faster is the easy one - blow hot air on it, or cup your hands around it (without touching it) so the heat of your hands warms the ice, you can take turns putting your hands around the cubeYou can also redirect light to the cube of ice, intensifying the heat of the lightLike a magnifying glass pointing sunlight on the iceMaking it melt slower without touching it, the assumption is you can't have anything touch the ice - cover it with a cupThe ice will cool the inside of the cup making the ambient temperature around the ice lower, therefore the ice will melt slowerThe smaller and more insulated the cup the better, if you can chill the cup that will also delay the ice from meltingWhat you are trying to make is a space around the ice to minimize the heat transfer.
Since the ratios are 1:1:3 there are five possibilities, so the probability that the tube is selected from A is 1/5, from B 1/5 and from C 3/5 So the answer to (i) is 1/5 The probability that the tube is defective is the sum of the products of the probability that a tube is selected from a specific machine times the probability of a defective from that machineFor A 0.10 0.20 0.02 For B 0.10 0.20 0.02 For C 0.20 0.60 0.12 Total 0.12 + 0.02 + 0.02 0.16 The probability that it comes from A given that it is defective is 0.02/0.16 0.125
