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  • Background information: I am studying events and subspaces, and I have a question about Events being a subset of the subspace. I am new to discrete mathematics, so sorry if I couldn't word my question more professionally.
  • Logical Question: Considering the below example, why the subset events are increasing and decreasing one after another? For example, it starts with (1,5) then goes to (2,4), but why not going to (1,4), (1,3)? I mean imagine 2 dice, you are not gonna get exactly 1 and 5, the number will vary, so it can be 1 and 3 or 1 and 2, but it is not listed.

Example:

Experiment: Rolling 2 dice

Sample space: S = {1,…,6} × {1,…,6}

Event: The sum of the dice is 6

A = {(1,5),(2,4),(3,3),(4,2),(5,1)}

Agent 0
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1 Answers1

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Note that the event is specifically: Sum of the numbers of two dice is $6$.

Then, under this event, there can be only $5$ outcomes corresponding to this: $\color{red}{(1,5)}$ with sum as $6$; $\color{blue}{(2,4)}$ with sum as $6$ , and similarly, $\color{green}{(3,3),(4,2),(5,1)}$.

Note that $(1,4)$ is also checked, but it is not taken into the sample space $A$, because it doesn’t satisfy the condition required for it to be in $A$, i.e., the sum of the rolls are not $6$.

  • Thanks for your clarification, I don't know why my notes didn't include that "Sum of the numbers of two dice [should be] 6". The only thing that was mentioned regarding the event was that an "event is a subset of a subspace". – Agent 0 Dec 21 '17 at 05:48
  • I believe for every situation I can consider the number of possibilities so, for example, the outcomes leading to 7 then can be (1,6), (2,5), (3,4),(4,3),(5,2), and (6,1). Thus, anything that adds up to 7, so 1+6, 2+5, etc. – Agent 0 Dec 21 '17 at 05:51