Independence

funnybabe

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Oct 17, 2012
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Greetings all,

I have this question I am working on but I am wondering if I am correct in my answer. The question asks:
Suppose a fair die has been thrown once. Let A be the event of an odd number to appear, and B be the event of an even number to appear, and C to be the event of a number greater than 4 to appear. It lists some statements to choose from which relate to independence.

I think the answer is that A and B are independent and that A and C, B and C are not independent.

Am I thinking about this correctly?
thanks!
 
I have this question I am working on but I am wondering if I am correct in my answer. The question asks:
Suppose a fair die has been thrown once. Let A be the event of an odd number to appear, and B be the event of an even number to appear, and C to be the event of a number greater than 4 to appear. It lists some statements to choose from which relate to independence.
I think the answer is that A and B are independent and that A and C, B and C are not independent.

Independent events, \(\displaystyle X\,\,\& \,Y\) have the property that \(\displaystyle \mathcal{P}(X\cap Y)=\mathcal{P}(X)\cdot\mathcal{P} (Y)\)

Now rethink your answers.
 
Independent events, \(\displaystyle X\,\,\& \,Y\) have the property that \(\displaystyle \mathcal{P}(X\cap Y)=\mathcal{P}(X)\cdot\mathcal{P} (Y)\)

Now rethink your answers.
The question isn't a computation question so I still think A and B are independent of each other because if I roll the dice, it is either an odd number or an even number. The C part is dependent on whether it is over 4 and in this case, since A is odd, if it 5 then it would be A and C
 
I figured out the answer and it is A and C are independent, B and C are independent but A and B are NOT independent. I am not sure why this is true because I thought A and B are independent of each other since they are odd or even. If anyone can explain this as it was more a conceptual question. thanks!
 
I figured out the answer and it is A and C are independent, B and C are independent but A and B are NOT independent. I am not sure why this is true because I thought A and B are independent of each other since they are odd or even. If anyone can explain this as it was more a conceptual question. thanks!

Here is an informal test. If you know that the number showing is odd does that effect its being even?
If so then the events are dependent. To be independent the one event being known has no effect on the other.

Knowing the number is odd does not effect of it being greater than four.
Events \(\displaystyle A~\&~B\) are dependent. Events \(\displaystyle A~\&~C\) are independent.
 
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So is flipping a coin and determining if it's heads or tails is dependent?
My book has defined independence as "if knowing that one had occurred, gave us no info about whether the other had occurred".

I can then see how this question makes sense. I think I was getting confused because I thought flipping coins was independent but the result is independent if you flip it multiple times since if rolling heads on the first doesn't have any affect on the 2nd roll
 
Defined independence as "if knowing that one had occurred, gave us no info about whether the other had occurred".
CORRECT! even though it is badly( miss-leadingly) worded.

So is flipping a coin and determining if it's heads or tails is dependent?
I can then see how this question makes sense. I think I was getting confused because I thought flipping coins was independent but the result is independent if you flip it multiple times since if rolling heads on the first doesn't have any affect on the 2nd roll
NO! The flips of a coin are independent trials.
"flipping heads on the first turn doesn't have any affect on the 2nd flip"
 
That reminds me of the old chestnut:
"The probability of a coin coming up heads on any one flip is 1/2. If the coin has come up heads 9 consecutive flips, what is the probability it will be heads on the tenth flip?"
 
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