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March 25th, 2016, 12:41 PM   #1
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Multiple Occurrences of Negative Events

Suppose we have a ball which has a chance of being dropped and a chance of remaining where it is. Let the chance of the ball dropping be y and let the chance of the ball remaining where it is be a. Thus the chance of the ball dropping four times is y x y x y x y. One might suggest doing the same with a, but something seems off. How could the ball 'not drop' multiple times, this is not the same as 'not getting heads' which constitutes a different event 'getting tails' because in this cause 'not dropping' is the same as saying 'no relevant event is happening'.

This is obviously a negative event, in the sense that it is an event constituted by something not happening. How many times does this event occur, every second? How can we treat it as an event when it is by definition the lack of an event, doesn't this seem rather like treating nothing as something? Are negative events just mathematical devices? If so, why do we treat them like genuine events?
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March 25th, 2016, 03:55 PM   #2
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The whole scenario makes sense if there are discrete attempts to drop the ball.
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March 25th, 2016, 05:49 PM   #3
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But there could just as easily not be.
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March 26th, 2016, 09:58 AM   #4
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When assigning a probability to an event you need to define limits for your "trial". For example "Suppose we have a ball which has a probability y of being dropped in the next hour (day, week, year whatever). Or "Suppose we have a ball which has a probability a of remaining where it is before teacher returns to the classroom (next fall of snow)". For each case, either the ball remains to the end of the "trial" or it drops when you perhaps replace it for a new "trial".
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March 26th, 2016, 10:48 AM   #5
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Quote:
Suppose we have a ball which has a chance of being dropped and a chance of remaining where it is.
The word chance is imprecise and hardly used in maths, but plays a part in the interpretation of physical processes, ie in Physics.
Note the other respondents used the word probability which is tightly defined.

Chance and probability do not mean the same.
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