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greenatstats
11-02-2005, 12:08 AM
Hi Folks..just started stats 102. I'm getting a little stuck with the concept of sample space and events. Although I understand both ideas as I'm reading the text, I have a question that I can't seem to wrap my mind around. It goes like this: roll a six-sided dice. Sample space is 1,2,3,4,5,6 right? The question is how to define the following: events A=(1,4), B=(6), C= (1,2,3) and D= (2,3,5). At first I thought I had it by answering with the following:
The event A = (1,4) and has occurred when the dice is tossed and it shows a 1 or 4. It could also be defined as Event A=numbers not including 2,3,5 or 6Event B has occurred when the dice shows a 6 or B could also =numbers other than 6; C = ‘1,2 or 3’is rolled; and D occurs when the dice throw results in 2,3 or 5. As noted in Event A, each event can also be defined by what is not wanted.
Then I started second guessing myself and feel like I don't get it at all. The question I'm trying to answer also asks about which event forms a "partition" of the sample space...not sure what this means and can't find a definition. I look forward to any suggestions.
Thanks

quark
11-02-2005, 12:25 AM
Hi greenatstats,

You're on the right track. The sample space is {1,2,3,4,5,6}, and event A is rolling a 1 or 4. It could be defined as not 2,3,5 but one definition is enough and you want to be straightforward.

If you have a partition of the sample space, the union of the events will form the sample space and the events are non-overlapping.

greenatstats
11-02-2005, 09:21 AM
Thanks so much! Doing this course as distance learning without classmates is tough. I enjoy the course but sometimes just clarifying some of these questions bogs me down.