Two dice rolled. Let \(\displaystyle E\) be the event that the sum of the outcomes is odd and \(\displaystyle F\) be the event of at least one \(\displaystyle 1\). Interpret the events \(\displaystyle EF\), \(\displaystyle E^cF\), and \(\displaystyle E^cF^c\).
This is how I did it. I started by defining the sample space of each event.
\(\displaystyle E = \{(1,2), (1,4), (1,6), (2,1), (4,1), (6,1), (2,3), (2,5), (3,2), (5,2), (3,4), (3,6), (4,3), (6,3), (4,5), (5,4), (5,6), (6,5)\}\)
\(\displaystyle F = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (6,1), (5,1), (4,1), (3,1), (2,1)\}\)
I treat \(\displaystyle EF\) as \(\displaystyle E\) AND \(\displaystyle F\). (I could be wrong)
In this case, I think that it asked to find the intersection between the two events. In other words, to find the outcomes in \(\displaystyle E\) that are also in \(\displaystyle F\).
\(\displaystyle EF = \{(1,2), (1,4), (1,6), (2,1), (4,1), (6,1)\}\)
The book agrees with my solution. So far so good.
The answer for the next event is obvious.
\(\displaystyle E^cF = \{(1,1), (1,3), (1,5), (5,1), (3,1)\}\). However the book is slightly different, \(\displaystyle E^cF = \{(1,1), (1,3), (1,5), (5,1), (3,1), (1,1)\}\).
Is there a necessity to repeat \(\displaystyle (1,1)\)? I don't understand why!? Could be a typo?
The last event is also obvious, but tedious to write.
\(\displaystyle E^cF^c = \{\) any outcome that is not in \(\displaystyle E\) and also not in \(\displaystyle F\) \(\displaystyle \}\)
Thank you guys in advance.
This is how I did it. I started by defining the sample space of each event.
\(\displaystyle E = \{(1,2), (1,4), (1,6), (2,1), (4,1), (6,1), (2,3), (2,5), (3,2), (5,2), (3,4), (3,6), (4,3), (6,3), (4,5), (5,4), (5,6), (6,5)\}\)
\(\displaystyle F = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (6,1), (5,1), (4,1), (3,1), (2,1)\}\)
I treat \(\displaystyle EF\) as \(\displaystyle E\) AND \(\displaystyle F\). (I could be wrong)
In this case, I think that it asked to find the intersection between the two events. In other words, to find the outcomes in \(\displaystyle E\) that are also in \(\displaystyle F\).
\(\displaystyle EF = \{(1,2), (1,4), (1,6), (2,1), (4,1), (6,1)\}\)
The book agrees with my solution. So far so good.
The answer for the next event is obvious.
\(\displaystyle E^cF = \{(1,1), (1,3), (1,5), (5,1), (3,1)\}\). However the book is slightly different, \(\displaystyle E^cF = \{(1,1), (1,3), (1,5), (5,1), (3,1), (1,1)\}\).
Is there a necessity to repeat \(\displaystyle (1,1)\)? I don't understand why!? Could be a typo?
The last event is also obvious, but tedious to write.
\(\displaystyle E^cF^c = \{\) any outcome that is not in \(\displaystyle E\) and also not in \(\displaystyle F\) \(\displaystyle \}\)
Thank you guys in advance.
