How to relate P(F) with P(F') where F' is F's closure (P(F)\neq 0)

[rukawakaede]

As title:

How do you relate P(F) with P(F') where F' is F's closure.

Conditions: $$P(F)\neq 0$$ and F non-empty.

My thought is P(F)=P(F').

Is this true?

 

[rukawakaede]

Now I understand that this depends on the probability measure and of course the set F itself. there is no general conclusion that could be draw for this situation.

 

[g_edgar]

In general, since F is a subset of its closure, the probability of F is less than or equal to the probability of the closure.

 

[rukawakaede]

In general, since F is a subset of its closure, the probability of F is less than or equal to the probability of the closure.

yes. thank you.

 

[blue_raver22]

No, this is not necessarily true. P(F) and P(F') may not be equal because they represent different probabilities. P(F) represents the probability of event F occurring, while P(F') represents the probability of event F' occurring. F' is the closure of F, meaning it includes all possible outcomes that are a result of event F. Therefore, F' may have a larger or smaller probability than F, depending on the specific events and their probabilities. For example, if F is the event of rolling a 6 on a standard die, P(F) is 1/6. However, if F' is the event of rolling an even number on a standard die, P(F') is 3/6 or 1/2. In this case, P(F) and P(F') are not equal.