Posted by **mark** on Sunday, March 25, 2007 at 8:40am.

In an experiment, a pair of dice is rolled and the total number of points observed.

(a) List the elements of the sample space

(b) If A = { 2, 3, 4, 7, 8, 9, 10} and B = {4, 5, 6, 7, 8} list the outcomes which comprise each of the following events and also express the events in words: A¢, A È B, and A Ç B.

(c) Use Venn diagrams to show the different events

The sample space would consist of the following

(1,1),(1,2)...(1,6)

(2,1),(2,2)...)2,6)

..

..

(6,1).........(6,6) there are 36 of these

for your b) I don't know what you mean with your symbols. I assume you probably want the intersection and union of these sets.

A∩B would be the "intersection" of the two sets, that is, all those elements that are found in both the first set AND the second set. I see that would be {4,7,8}

AUB, A "union" B, is the set of elements that are found in either A OR B.

That would be {2,3,4,5,6,7,8,9}

To draw the Venn diagram, draw two overlapping circles.

Place the numbers 4,7, and 8 in the overlapping part, the "intersection".

Place the remaining numbers in their corresponding regions of the circles.

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