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November 6th, 2017, 04:20 AM   #1
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How to calculate the Sample Space S

Hi,

I'm currently studying up on the basics of probability. One thing that keeps eluding me is how to properly calculate the sample space.

From the examples I have seen, they have visually done this. However, this is, of course, not possible or practical if one wants to create formulas or programmatically calculate the sample.

This is how far I have come in trying to understand it.
Feel free to correct me if I'm wrong.

Calculate the sample size for two 6 sided dices.

Toss 1 Sample Size: (6*6)POWER(1) // How do you make text superscript in this forum?


Toss 2 Sample Size: (6*6)POWER(2)

Toss 3 Sample Size: (6*6)POWER(3)

Etc.

Is this correct? If not, what is the correct way of calculating the sample size?

Last edited by skipjack; November 6th, 2017 at 07:16 AM.
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November 6th, 2017, 04:29 AM   #2
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Math Focus: Yet to find out.
Are you just trying to find the total number of outcomes, or do you want to list the outcomes?

The total number of outcomes is indeed 6^2. If you throw a die once, how many outcomes are there? 6. Record the number. Now throw again, how many outcomes? 6 again. Record the number.

So the sample space will consist of all pairs of numbers possible from tossing a die twice. It will look something like this: S = {(1,1), (1,2),..., (6,6)}. I leave you to fill in the details (it’s tedious, but worth doing once if you’re just starting).

Last edited by skipjack; November 6th, 2017 at 07:14 AM.
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November 6th, 2017, 04:44 AM   #3
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Quote:
Originally Posted by Joppy View Post
Are you just trying to find the total number of outcomes, or you want to list the outcomes?

The total number of outcomes is indeed 6^2. If you throw a die once, how many outcomes are there? 6. Record the number. Now throw again, how many outcomes? 6 again. Record the number.

So the sample space will consist of all pairs of numbers possible from tossing a die twice. It will look something like this: S = {(1,1), (1,2),..., (6,6)}. I leave you to fill in the details (it’s tedious, but worth doing once if you’re just starting).
Hi Joppy,

Thank you for your quick response. I'm just trying to find out the total number of outcomes. However, I'm still a bit unclear about finding out the actual number of possible outcomes for 1 toss vs multiple tosses.

Let's take another example and perhaps that will help clear things up for me.

Let's take two dice. We have a normal 6 sided dice. And a 4 sided dice.

The total possible outcomes for these two dice are 6 * 4 = 24 ?

Now to factor in X amount of tosses would this be done with 24^x ?

Toss 1: 24^1
Toss 2: 24^2
Toss 3: 24^3
etc.

Last edited by skipjack; November 6th, 2017 at 06:32 AM.
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November 6th, 2017, 04:59 AM   #4
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Quote:
Originally Posted by Joppy View Post
Are you just trying to find the total number of outcomes, or do you want to list the outcomes?

The total number of outcomes is indeed 6^2. If you throw a die once, how many outcomes are there? 6. Record the number. Now throw again, how many outcomes? 6 again. Record the number.

So the sample space will consist of all pairs of numbers possible from tossing a die twice. It will look something like this: S = {(1,1), (1,2),..., (6,6)}. I leave you to fill in the details (it’s tedious, but worth doing once if you’re just starting).
Hi Joppy,

Thanks for your quick answer.

I am just looking to find the total number of outcomes, i.e. not list them. I am stilling having a bit of trouble grasping it all.

Let's use another example of using a 6 sided dice and a 4 sided dice.

Is the following correct?

The total possible outcomes of these two diced are
6 * 4 = 24 possible outcomes.

To calculate X tosses, does it work like this?

1 toss: 24^1 = 24
2 toss: 24^2 = 576
3 toss: 24^3 = 13824
4 toss. 24^4 = 331776
etc.

Last edited by skipjack; November 6th, 2017 at 07:14 AM.
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