how is probability by experiment different from probability by calculation?

Answer 1

An example I like is: playing the lottery. Buy tickets for six weeks. Loose all six weeks. The experimental probability of "winning the lottery" is 0/6 = 0. The actual, or theoretical, probability is calculated using the binomial coefficient, and is usually around a chance of 1 in 5 million (or 6 million or 10 million or ... depending on which lottery you talking about). The first value 0 is the experimental probability: do an experiment and estimate the chance.

Answer 2

It's not that the two values are vastly different in meaning. As stated above, repeated experimental results should yield the same value as calculated. The reason the distinction exists is that, throughout the history of science, it has always been important to be clear about how one came to a conclusion. Not so much for that person's benefit, but if that person wrote a report, and someone in a completely different time and place with no previous knowledge of the experiment/calculation would know at a glance whether the data is calculated or arrived at by experiment.

Answer 3

What's the probability of the total of two dice being 7?

By calculation: Out of the 36 possible results from throwing two dice, six have a total of 7. Answer: 1/6.

By experiment: Throw two dice N times. Let X be the number of times the total happens to be 7. The estimated probability is X/N.

Answer 4

"probability" by experiment is more acurately described as "statistics." Experimentation is the effort to estimate a probability distribution. But experiments have limitations, particularly in representing all the conditions that may impact a dependent variable.

Likewise, probability by calculation is the attempt to represent variables by closed form distributions. The normal distribution is often used to represent many types of variables, but most events are not normally distributed. Many inferences may be made using probability distributions, particularly when trying to predict future events.

Answer 5

This is a common argument I use with those who say "it couldn't have just happened." In fact, it could have, and, in fact, it MUST have, or we wouldn't be here talking about it. As the post by "No Chance" shows, they commonly fire an arrow at the wall, then draw a target around it and call it a bull's eye. The fact remains, despite the incredible odds, SOMEONE wins the lottery. It doesn't mean that a grand planner conspired to make those numbers come up for that person. People only see what hits, they never see what misses.

Answer 6

In experiments you have always fluctuations from the theorethic values. But there is the "Big numbers law" that states that if you repeat the experiment a high number of times the result is getting closer to the theorethic figure.

Answer 7

You already have the all good input already. How come I don't have Yahoo answer when I was a student....

There is also sampling error; in statistics the p value/confident interval etc show how significant the outcome of your experiment or how close it is to the true values.