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March 30th, 2016, 06:48 PM   #1
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Sample Space

Identify the sample space of the probability experiment: rolling a pair of 12-sided dice (with sides numbered 1-12) and observing the total number of points of each roll.


Is this question asking that I do (1,1) (1,2)(1,3)(1,4)(1,5)(1,6)(1,7)(1,(1,9) and so forth?
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March 31st, 2016, 05:20 AM   #2
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Sample Space
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March 31st, 2016, 11:29 AM   #3
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There are 12*12 = 144 possible outcomes. Here are the frequencies for each point total:

2: 1
3: 2
4: 3
5: 4
6: 5
7: 6
8: 7
9: 8
10: 9
11: 10
12: 11
13: 12
14: 11
15: 10
16: 9
17: 8
18: 7
19: 6
20: 5
21: 4
22: 3
23: 2
24: 1

Note that it's symmetrical. Regardless of how many sides the dice have, the mean, median, and mode are the same and are the sum of 1 and the highest number.
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March 31st, 2016, 01:10 PM   #4
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Quote:
Originally Posted by alymrod View Post
Identify the sample space of the probability experiment: rolling a pair of 12-sided dice (with sides numbered 1-12) and observing the total number of points of each roll.
This is a poorly worded question. No experiment has a unique sample space, one that can definitively be called "the" sample space. A sample space is merely a list of all the different ways, THAT ARE SIGNIFICANT TO YOUR ANALYSIS, that describe the set of possible results. Different interests might require different ways to do this.

If you flip a coin, A sample space is {H,T}. If you are interested in seeing whether the phases of the moon (call them Q1, Q2, Q3, and Q4) affect the con flip, A PERFECTLY ACCEPTABLE sample space is {HQ1, HQ2, HQ3, HQ4, TQ1, TQ2, TQ3, TQ4}. All that is important to be a sample space, is that every possibility is included in exactly one member of that space.

But the point of having a sample space is to define a probability for each member. Some choices might make that easier. A sample space for your experiment is the set of integers from 2 to 24. But it isn't immediately obvious what the probabilities are. Another is the set of 12*12 combinations for the "first die" and the "second die." These are all equally probable so they have probabilities 1/144. You can use this to establish the probabilities for the first one I mentioned, if you can figure out how many of the second correspond to each of the first.
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