MadSci Network: Physics
Query:

Re: why say the probablity is 50%,when someboby don't one thing?

Date: Wed Mar 14 09:18:49 2007
Posted By: Mark Huber, Assistant Professor, Mathematics and Statistics
Area of science: Physics
ID: 1173754830.Ph
Message:

Question: why say the probablity is 50%,when someboby don't one thing?
From: meng
Grade: grad (science)
City: NJ, State/Prov.: JS Country: China

usually,when we ask somebody a question about what WILL happen,if he or she totally do not have idea about it,he or she says the probability is 50%. For example,"the probability of rain tomorrow is 50%" ,but I do not think it a correct method to explain not knowing.



Probabilities measure how likely events are to occur. Usually, the basic idea of probability comes from physical processes where symmetry is involved. For instance, suppose I have a coin that I believe to be roughly symmetric. If I choose a side of a coin, then it is reasonable to say that when I flip the coin in the air, there is roughly a 50% chance that it will land on a side I chose.

Now, suppose you are asked a question that you have no idea what the answer is. For example, if I asked you whether my favorite color was either green or blue (and no other color is allowed), you would have no idea as to the answer. In a sense, you might as well flip a coin to decide how to answer the question. It that way, when you have no information whatsoever about the answer, it is reasonable to say that it is 50%.

On the other hand, often you do know something about the question, at which point that information must be included in your estimate of the probability. If I had a symmetric six sided die with sides labeled 1, 2, 3, 4, 5, and 6, then it would be reasonable to say that there was only a 1/6 chance of a 1 coming up. It would be unreasonable to say that there was a 50% chance of a 1 coming up because it either does or does not come up. Here saying there is a 50% chance ignores what we know about the die. [note added by MadSci Admin: And if, in the previous paragraph, we allowed the possibility of the colors green, blue, orange, red, yellow, and purple, the probability of guessing my favorite color would also be 1/6, just like the six sided die.]

In the same way, with the rain example, saying that there is a 50% chance of rain ignores what you know about rain in your area beforehand. I know next to nothing about the climate of China, but in the state of Oregon in the US where I grew up about half of the days were rainy. But during the summer there were far fewer rainy days, and during the winter there were more. Knowing whether it was summer or winter would allow me to change my guess at the probability of rain.

Even with this knowledge, my estimate of the probability would not be exact, in the same way that you could estimate the height of a mountain by looking at it, but without taking extensive measurements, you could not know the height of a mountain exactly. If I had data about temperature, wind speed, humidity, satellite photos, or other pieces of evidence, my estimate of the probability of rain would be much better.

So saying the probability is 50% is like saying that the two outcomes are symmetric in every way, and you have no information about which is the more likely outcome. This can sometimes be true, but usually you have more information at your disposal to give a better estimate of the probability.

Mark Huber


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