15 replies to this topic

[Harut]

here are some interesting facts from my statistics book.
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Probabilities that Challenge Intuition

In certain cases, our subjective estimates of probability values are dramatically different from the actual probabilities. Here is a classic example: If you take a deep breath, there is better than a 99% chance that you will inhale a molecule that was exhaled in dying Caesar's last breath. In that same morbid and unintuitive spirit, if Socrates' fatal cup of hemlock was mostly water, then the next glass of water you drink will likely contain one of those same molecules. Here’s another less morbid example that con be verified: In classes of 25 students, there is better than a 50% chance that at least 2 students will share the same birthday.

Six Degrees of Separation

Social psychologists, historians, political scientists, and communications specialists are among those interested in "The Small World Problem": Given any two people in the world, how many intermediate links are required in order to connect the two original people? Social psychologist Stanley Milgram conducted an experiment using the U.S. mail system. Subjects were instructed to try and contact other target people by mailing an information folder to an acquaintance who they thought would be closer to the target. Among 160 such chains that were initiated, only 44 were completed. The number of intermediate acquaintances varied from 2 to 10, with median of 5. A mathematical model was used to show that if those missing chains were completed, the median would be slightly grater than 5.

Cost of Laughing Index

There really is a Cost of Laughing Index (CLI), which tracks costs of such items as rubber chickens, Groucho Marx glasses, admission to comedy clubs, and 123 other leading humor indicators. This is the same basic approach used in developing the Consumer Price Index (CPI), which is based on a weighted average of good and services purchased by typical consumers. While standard scores and percentiles allow us to compare different values, they ignore any element of time. Index numbers, such as the CLI and CPI, allow us to compare the value of some variable to its value at some base time period. The value o fan index number is the current value, divided by the base value, multiplied by 100.

Buying Cars

For buying a new or used car, an excellent reference is the reliability data compiled and reported by Consumer Reports magazine. Frequency-of-repair data are based on 10 million pieces of data collected from thousands of readers. Statisticians analyze the data for patterns that lead to lists of both reliable cars and cars that should be avoided. Consumers Union President Rhoda Karpatkin writes, "Because numbers describe so much of our work, it should be no surprise that statisticians are key to that process."

Authors Identified

In 1787-1788 Alexander Hamilton, John Jay, and James Madison anonymously published the famous Federalist papers in an attempt to convince New Yorkers that they should ratify the Constitution. The identity of most of the papers' authors became known, but eh authorship of 12 of the papers was contested. Through statistical analysis of the frequencies of various words, we can now conclude that James Madison is the likely author of those 12 papers. For many of the disputed papers, the evidence in favor of Madison's authorship is overwhelming to the degree that we can be almost certain of being correct.

Independent Jet Engines

A three-engine jet departed from Miami International Airport en route to South America, but one engine failed immediately after takeoff. While the plane was turning back to the runway, the other two engines also failed, but the pilot was able to make safe landing. With Independent jet engines, the probability of all three failing is only 0.0001^3, or about one chance in a trillion. The FAA found that the same mechanic who replaced the oil in all three engines incorrectly positioned the oil plug sealing rings. A goal is using three separate engines is to increase safety with independent engines, but he use of a single mechanic caused their operation to become dependent. Maintenance procedures now require that the engines be serviced by different mechanics.
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i'll add at some later day.

[Sip]

WOW! So Harut jan, let me see if you have been paying attention ... in a class of 25, what is the probability that someone will have the same birthday as you?

[Azat]

It is just about 55%

Here is the chart for you
and here is the formula

1-(365x364x363x...x341)/(365)to the 25 power

[Harut]

sorry Sip, i didn't see your question.
well, Azat gave it already.

[Sip]

Sorry guys ... but you are wrong Read the question and what azat posted carefully!

By the way, there are 3 ways of interpreting that question. Any one of those would be a valid answer I think (considering how I have asked it).

[ October 24, 2002, 12:28 AM: Message edited by: Sip ]

[Harut]

1/365

[Sip]

I don't think so. But why 1/365?

[Harut]

i thought this is one of those interpretations.

no matter how big the class is, if we pick someone there would be 1/365 probability.

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[Sip]

Ok then maybe there are 4 ways to interpret ... fair enough. The other trivial way, is that if you are in the class, then the probability is 100% (you, yourself )

Now for the other 2 cases:

1) You are in the class ... what is the probability that someone else (other 24) has same birthday as you.

2) You are not in the class ... what is the probability that someone in the class (25 people total) has the same birthday as you.

[Azat]

duh.

that is even easier
24/365 and 25/365

[Sip]

He he he ... I knew this was going to cause confusion

So if we continue your formula, if there are 365 people in the class, the chance of someone else having the same birthday would be 365/365 (100%) ... well, we all know that doesn't have to be true.

In a class with 366 people, at least 2 people MUST have the same birthday (the table Azat posted) ... but they don't have to have the same birthday AS YOU!

Note: I guess its obvious we are ignoring leap years and Feb 29 birthdays .... assume 365 days, and that all days are equally likely.

[Azat]

Okay Okay. Call me an idiot.

I think I got it.(This should have been much easier for me as I have a degree in Stats and Proj Mgmt, but I am a bonehead and have not used it in the last 10 years since I have been out of school)

The chance that a person does not share the same birthday as you is 364/365 or 99.7% or 1-(364/365) to get the probability of 1 person sharing your birthday.

So if you have 24 people in the room the formula is 1-(364/365)^24 or 6.37%. with 25 in class it is 6.63%. and it is 63.2% if there are 365 people in the room.

(I need to go back to school as I am forgetting all my stats stuff)

[Sip]

Azat, I am proud of you! I realized the other day, I have forgotten most of calculus!!! Thank GOD for mathcad (It solved some 3 BIG derivatives for me symoblically!!!)

[Harut]

what's the probability that the Gogzilla is standing right outside of your door?

[gamavor]

One of the solutions closely corresponds to the following question: Is there any chance for a little boy who falls down from a 20 story building to survive?

[Harut]

hehe

actually i was looking for that solution.