Question 824599: hello everyone
i have a final exam tomorrow and i have this question in one of the old exams that i couldn't understand how to solve it.
A red die and a green die are thrown, and the numbers of each are noted.
Which pairs of the following events are mutually exclusive?
E={both are even}, F={both are odd}, G={sum is 2}, H={sum is 4},
I={sum is greater than 10}.
can you explain it for me ?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Ok, here we go :-)
We assume that our red (r) and green (g) dice are fair and independent. This means that each possible outcome (r,g) is equally likely. Note that each of r and g can be any of the integers from 1 through 6. Here is a listing of all the joint possibilities for (r,g):
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Now there are 36 possibilities for (r,g) because there are 6 possibilities for r, and for each outcome for r, there are 6 possibilities for g. So, the total number of joint outcomes (r,g) is 6 times 6 which is 36. This is called the sample space for this probability experiment. With all this in mind, let's consider the sets your problem uses.
1) E={both are even} = { (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6) }
2) F={both are odd} = { (1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5) }
3) G={sum is 2} = { (1,1) }
4) H={sum is 4} = { (1,3), (2,2), (3,1) }
5) I={sum is greater than 10} = { (5,6), (6,5), (6,6) }
Which pairs of these events are mutually exclusive? Mutually exclusive events means that their set intersection is 0, that is, they have no set elements in common. Therefore,
Events E and F are mutually exclusive
Events E and G are mutually exclusive
Events F and I are mutually exclusive
Events G and H are mutually exclusive
Events G and I are mutually exclusive
Events H and I are mutually exclusive
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