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Prior probability definition statistics of sexual immorality

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By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. I want to teach a short course in probability and I am looking for some counter-intuitive examples for it.

Results that seems to be obviously false but they true or vice versa I have also found some advanced examples. Could you please help me to make a list of these phenomena? It's very exciting to read your examples The most famous counter-intuitive probability theory example is the Monty Hall Problem. The "Prior probability definition statistics of sexual immorality" is that it does matter whether or not you switch. This is initially counter-intuitive for someone seeing this problem for the first time.

A beginner in probability would expect the answers to both these questions to be the same, which they are not. Math with Bad Drawings explains this paradox with a great story as a part of a seven-post series in Probability Theory. If it is the case that P is more likely to win over Q, and Q is more likely to win over R, is it the case that P is likely to win over R?

The answer, strangely, is no. Her attendant tosses a fair coin and records the result.

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Given that Sleeping Prior probability definition statistics of sexual immorality is epistemologically rational and is aware of all the rules of the experiment on Sunday, what should be her answer? In an urn, you have 90 balls of 3 colors: All the other balls are either blue or yellow.

However, it can be shown that there is no way to assign probabilities in a way that make this look rational. One way to deal with this is to extend the concept of probability to that of imprecise probabilities. How many people should be in a room so that the probability of at least two people sharing the same birthday, is at least as high as the probability of getting heads in a toss of an unbiased coin i.

This is a good problem for students to hone their skills in estimating the permutations and combinations, the base for computation of a priori probability.

I still feel the number of persons for the answer to be surreal and hard to believe! Pupils should at this juncture be told about quick and dirty mental maps for permutations and combinations calculations and should be encouraged to inculcate a habit of mental computations, which will help them in forming intuition about probability. It will also serve them well in taking to the other higher level problems such as the Monty Hall problem or conditional probability problems mentioned above, such as:.

A random person from the population is selected and is found to be tested positive for that disease. What is the real probability of that person suffering from the strange disease. This should be the starting point for introducing some of the work of Daniel Kahneman and Amos Tversky as no probability course in modern times can be complete without giving pupils a sense of how fragile one's intuitions and estimates are in estimating probabilities and uncertainties and how to deal with them.

However, the first person in line forgot his boarding pass and as a result decided to sit down in a random seat.

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The second person will do the following:. Each following person sits according to the same rules as the second person. Most people think the probability is very small and think there is a tiny chance of the th person's seat being left after all the people move around.

A while back, the xkcd blog posted Prior probability definition statistics of sexual immorality problemwhich I found fascinating. Usually when I re-tell it, I do so slightly differently from the original author:. I have written each number in a separate envelope. By fair coin toss, I select one of these two envelopes to open, revealing that number.

I then ask the question "Is the number in the other envelope larger than this one? You win if you guess correctly. Note, that is a strict inequality.

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Now, the solution to this starts out with a double-integral, so depending on the level of the class you're teaching it may not be appropriate. I find that almost anything about probability is counter-intuitive to my college students on first encounter. Possibly this may depend on your audience. Here are a few examples:. This is after an hour-long lecture on the subject. Once I had a student so bamboozled by it that she called up the national meteorology service for a consultation.

I've never had anyone in Prior probability definition statistics of sexual immorality class intuit the correct answer on first presentation. Are these equally likely outcomes? This can be repeated with the same result with similar follow-up questions. At each step, you can either choose to leave the game with all the sweets in the pot, or you can continue the game.

If you continue, a fair coin is flipped, and if it comes up heads then the sweets in the pot are tripled, but if it comes up tails then the pot is emptied. If you can play this game only once, how many sweets would you be willing to pay to play? And how should you play? Assume that you want to get the most sweets possible. Thus you should not stop. But that is stupid; if you never stop you will never get any sweets!

So when to stop? Worse still, a correct analysis will tell you that no matter how many sweets you pay, you can play in such a way that the expected number of sweets you leave with is more than what you paid!

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