You are not feeling well, so you go to the doctor and you test positive for a disease effecting .1% of the population. The test you took correctly identifies 99% of the people that have the disease and is only wrong 1% of the time What is the probability that you actually have the disease Answer Intuitively, most people would say you have a 99% probability of having a disease you tested positive for if the test is right 99% of the time, however… The disease affects .001% of the population or 1 out of 1000 people And the test incorrectly identifies 1% of the population as having the disease or .01, which is 10 people out of 1000 …and you know that .1% of the population has the disease and .1% = 1/1000 but 10 of those people are incorrectly identified as having the disease which gives you a population of 990 people then I calculated 1% of 990 and got 9.9% Therefore, I think the chance of actually having the disease is 9.9 % In the video he solved the problem differently by saying: “the sample size is 1000 people and 1 person out of the 1000 people has the disease but out of the 999 other people 1% or 10 people would falsely be identified as having the disease so that makes a group of 11 people where only 1 person has the disease, so the chance of you actually having the disease is 1 in 11 people or 9%. Part II, Now assume you go to another doctor and take the same test what is the probability that you have the disease now??? In part II he used bayes theorem to calculate the new probability which turned out to be 91%!!!
So, are we getting a new puzzle anytime soon? It's nice to at all time have one of these threads active in the science section. Anyway, a puzzle from me: Aliens are invading earth, and they're all flying the same model of space ship. The combined forces of earth haven't figured out how many of these space ships the aliens have got, but they have figured out their numerical system, and noticed that each space ship has a production serial number. Before the final push against the aliens, they need to make an assumption of how many space ship the aliens have got. Humans have shot down 15 space ships. With the following serial numbers: 261, 449, 524, 415, 406, 298, 41, 447, 185, 194, 267, 331, 401, 132, and 231. Based on this information, how many space ships have the aliens produced in total of this model?
Cannot be bothered to do the maths, but many thousands have been produced. Edit. But only a tiny fraction would have invaded the earth. If 1,000 were on earth then would expect serial number over 500 would be shot down.
Perhaps the aliens didn't send ships with contiguous serial numbers. That may mean that we killed all 15 they sent. Perhaps the aliens put 15 dummy ships with random serial numbers in low orbit to test our capabilities at shooting them down. Perhaps the aliens put 15 dummy ships with random serial numbers in low orbit to fool us into thinking there were less than 1000. Why are we shooting them down before we know their intentions? If their intentions were good, Donald Trump screwed up big time by shooting them down. If their intentions are bad, shooting down 15 probably would have been impossible. Any alien race capable of building ships capable of interstellar travel would have shielding to deter any human "shooting down" nonsense. Therefore, Trump lied to us all to give us a false sense of security before our ultimate demise.
Assume production has stopped, and they've sent their entire fleet, so the ships shot down were totally at random. Not one is being kept back at their home planet. Also assume the aliens screwed up on the intelligence when it came to the serial numbers, so they're not trying to fool us on this.
Just done the maths. If we assume that they sent spaceships with consecutive numbers then they probably sent just over 524 spaceships. This could mean 600 or so. If they sent more than 600 then I would expect one to have been shot down with a higher number. Of course this also assumes none had been lost before arriving.
That would be the minimum number. That is if we assume the lowest number is 1. Otherwise it is a trick question.
Damn, that's really accurate. Didn't think anyone would come this close, care to show your method? So, i used a random number generator, numbers between 1-568, so 568 would be the absolute correct answer (but it's impossible/you have to be lucky to get the EXACT number anyway). https://en.wikipedia.org/wiki/German_tank_problem By using the frequentist approach, I got 558. Missing the correct answer with 10, pretty close. By using the bayesian approach, I got 563. Missing by 5, even closer. But you managed to miss by only 3. I'm curious how you did it, because this is impressive.
The minimum number would be 524, since that's the highest serial number. (The humans could have shot down the last produced space ship, but it's improbable when they only shot down 15.)
We know the lowest was off by 40. Applying the same "rule" to the highest give us ... oops, I should have come up with 564. Lowest 41 (off by 40) Highest 524 (off by 40?) 524 + 40 = 564 But really, it's pretty close to guessing. If they had shot down... Lowest 2 Highest 524 524 + 1 = 525 I'm sure the right way to do the problem is a lot more complicated than my way. What is the right way? What is the most accurate estimate?
Not so sure if there is a right way. The bayesian method is usually great. But there's a third method, pretty similar to how you did it, only difference being all the numbers are used, and find the average gap between each serial number. Then we get an estimate of 558. Missed by ten. This is one of those puzzles that have multiple solutions, and multiple different ways of solving it. And your method was the best in this example.
