Experiment: Make 1000 balls roll a board of nails and at the bottom of the incli

Question

Experiment: Make 1000 balls roll a board of nails and at the bottom of the inclined board, there are bins labeled (-10, -9, -8... 0, 1, 2 ... 10)

You make a mark to indicate how many balls fall into a certain bin.

You make a data column and at the end, you find that 100 balls ended up in the -5 bin.

You also find that 120 go into bin 4, 32 in bin 8, and so on.

Since you have a total of 1000 rolls, you then calculate the probability: 100 balls / 1000 rolls.

The probability of any ball ending up in the -5 bin turns out to be 10%.

Now the question: When you make a histogram of the probability (y-axis range from 0.0 - 1.0 because 0-100% and the x-axis is the bin numbers) in which there is a bar for each of the bin's probabilities (21 in total-- 0 included), is it plausible to add error bars to each bar? Is there a standard deviation for each bin's probability of ending up with a ball?

Explanation / Answer

Yes, it is plausible to add error bars to each bar in the histogram drawn based on the observed data.

Because, the data observed here is only one particular realization of the described random experiment, which means that the current 21 probability values that are observed in this experiment will change when we carry out yet another trial of the same experiment. And therefore, each of 21 probability values, themselves are random variables, whose value will change with different trials of the experiment. And, since every Random variable has its own Standard deviation, each bin's probability of ending up with a certain number of balls also has its own standard deviation.

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