- #1

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maybe i need a suggestion if the type i want to use down is correcty or not cuz i stucked...

I know that for A1,A2,An we have this type : P(A1andA2and....andAn)=P(A1)P(A2).....P(An) but how i can use this if i have sets?

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- Thread starter ParisSpart
- Start date

- #1

- 129

- 0

maybe i need a suggestion if the type i want to use down is correcty or not cuz i stucked...

I know that for A1,A2,An we have this type : P(A1andA2and....andAn)=P(A1)P(A2).....P(An) but how i can use this if i have sets?

- #2

Simon Bridge

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What is the definition of "independent" in this context? (Hint: in terms of probabilities.)

You have:

... you don't have to apply the relation to whole sets, the A1,A2,... form a set {A1, A2, ...}.P(A1andA2and....andAn)=P(A1)P(A2).....P(An) but how i can use this if i have sets?

if A and B are independent, then P(A)+P(B)=?

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- #4

Simon Bridge

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It boils down to how you read this bit:

Presumably "they" is x and y.

"{a,b} is independent", then I'd read that as outcome a is independent of outcome b... I don't think that {a,b} can be independent of {a,c} since they both contain a.

I read the question as saying that {a,b,c} may or may not not be independent, but {a,b} and {a,c} are.

Given that P(c)=0.3, what is P(a) and P(b)?

However: you are closer to the course than I am so you may have an extra insight.

- #5

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There is exactly one setting of x and y that makes it true.Wellifyou are interpreting it correctly - then how would the relation P[f∈{a,b}|f∈{a,c}] = P[f∈{a,b}] possibly hold? After all, the two sets have a member in common.

Aren't a, b and c atomic events? If so, they are therefore mutually exclusive, not independent. In probability space terms, a set of possible outcomes, like {a, b} constitutes a (nonatomic) event, and you want the events {a, b}, {a, c} to be independent."{a,b} is independent", then I'd read that as outcome a is independent of outcome b.

- #6

Simon Bridge

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I still think the phrasing is sloppy... which is why I'm uncertain about how I was reading the question.

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