2 dice rolled, sample space given: which mut. exclusive?

[flyingfreedom]

Two dice are rolled. A sample space which shows the possible sums is provided below:

Consider the following events:
A) The sum of the two dice is 6.
B) The first die rolled is a 4.
C) The sum of the two dice is 9.
D) The second die rolled is a 5.

Which of the two events given above are mutually exclusive?
A. A and B
B. A and C
C. B and C
D. B and D
I answered D but the correct answer is B.
The logic behind my answer is that rolling a 4 and a 5 when drawn as a venn diagram do not touch each other. ie. a 4 and a 5 aren't the same number
The logic behind it not being B is that the sum being 9 or 6 are not totally separated from each other. So to say, if I roll a five on the first... then for the second I could roll either a 1 or a 4 and get 9 or 6 as my final outcome.
Of course seeing that they do say 2 dice are being rolled that kind of suggests that sums of dice would be used.
Anyway some feedback on the definition of mutually exclusive and this questions would be totally awesome.

 

[tkhunny]

Re: mutually exclusive

Consider the following events:
A) The sum of the two dice is 6.
B) The first die rolled is a 4.
C) The sum of the two dice is 9.
D) The second die rolled is a 5.

You are saying that it is NOT possible to roll a 4 on one die and then roll a 5 on the other? Why not?

You are saying that it IS possible to roll a sum of 6, but have the same roll add up to 9 later?

 

[flyingfreedom]

Re: mutually exclusive

"You are saying that it is NOT possible to roll a 4 on one die and then roll a 5 on the other? Why not?"
A 4 and a 5 aren't the same number. I guess I would have to be talking about single roll experiments?


"You are saying that it IS possible to roll a sum of 6, but have the same roll add up to 9 later?"
when you roll let's say a 3 then depending on the next roll you could get either a sum of 6 or 9. They have some common outcomes like 3,4,5,6

actually I if someone could explain mutually exclusive in the context of this question I would probably understand it better.

 

[flyingfreedom]

Re: mutually exclusive

I guess the key phrase making me wrong here is "Two dice are rolled"

 

[pka]

Re: mutually exclusive

Mutually exclusive events are two events that are impossible to occur at the same time. In this problem A & C are surely mutually exclusive events.
Whereas, B & D are not mutually exclusive events. You can roll 4,5.

 

[tkhunny]

Re: mutually exclusive

I guess the key phrase making me wrong here is "Two dice are rolled"

That's it. It DOES help to answer the actual problem statement rather than makign up your own and being confused.