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# probability help watch

1. If A is independent from B, and B is independent from C, is A independent from C?
2. (Original post by Notnek)
Simple example - you have a coin and a dice:

A : Toss the coin and get heads
B : Roll the dice and get a 6
C : Toss the coin and get tails

What do you think?
Yes, but isn't it also possible in general for (say) A and C to be mutually exclusive (i.e. not independent) but for both to intersect separately with B such that A and B are independent and B and C are independent? In this case, A is independent from B, and B is independent from C, but A is not independent from C.
3. (Original post by SWISH99)
If A is independent from B, and B is independent from C, is A independent from C?
I don't think so. A and C could depend on each other and B could still be independent from both. For example:

A: Probability that it is raining right now.
B: Probability that I get a 6 when I roll a die.
C: Probability that I take an umbrella.
4. (Original post by old_engineer)
Yes, but isn't it also possible in general for (say) A and C to be mutually exclusive (i.e. not independent) but for both to intersect separately with B such that A and B are independent and B and C are independent? In this case, A is independent from B, and B is independent from C, but A is not independent from C.
My post was a counter example to the claim made by the OP, which is all you need to disprove it. I’m a bit confused by your post.
5. (Original post by Notnek)
My post was a counter example to the claim made by the OP, which is all you need to disprove it. I’m a bit confused by your post.
I think we are at cross-purposes. I took your event C to mean “toss the coin and get tails with the next throw”. Did you mean “toss the coin and get tails in the same throw as A”? If so I can see your point but then isn’t your C just A’ rather than being a separate event?
6. (Original post by old_engineer)
I think we are at cross-purposes. I took your event C to mean “toss the coin and get tails with the next throw”. Did you mean “toss the coin and get tails in the same throw as A”? If so I can see your point but then isn’t your C just A’ rather than being a separate event?
I just re-read my post and I see what you mean - I gave a bad example

I'll delete my post since TheMindGarage gave a correct example above.

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