1) A1 A2 be two events, show that P (A1 ∩ A2) ≤ P (A1)P

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Homework Help Overview

The discussion revolves around probability theory, specifically focusing on the relationships between events A1 and A2, and their intersections and unions. Participants are examining inequalities involving probabilities and questioning the validity of certain statements related to these events.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the original statements of the problems and are exploring the implications of specific cases, such as when A1 equals A2. Questions about the meaning of notation, such as A + B and /A, are also raised.

Discussion Status

The discussion is active, with participants seeking counterexamples to challenge the validity of the statements. Some have expressed uncertainty about the original problem statements, while others have confirmed their understanding of the issues at hand.

Contextual Notes

There is mention of potential errors in the transcription of the problems, and participants are considering the implications of these errors on their interpretations. The notation used in the problems is also under scrutiny, particularly regarding the complement and union of sets.

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1) A1 A2 be two events, show that P (A1 ∩ A2) ≤ P (A1) . P (A2)
2) show that P (A1 ∩ A2 ∩ ... ... An) ≤ P (A1) . P (A2) . ... ... ... ... P (An)
4)
show that P (A + B) + P (/ A + / B) = 1

I have problems with these exercises. I don't know if I copied them wrong.
thanks
 
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kezman said:
1) A1 A2 be two events, show that P (A1 ∩ A2) ≤ P (A1) . P (A2)
2) show that P (A1 ∩ A2 ∩ ... ... An) ≤ P (A1) . P (A2) . ... ... ... ... P (An)
4)
show that P (A + B) + P (/ A + / B) = 1

I have problems with these exercises. I don't know if I copied them wrong.
thanks

Why don't you look and see if you copied them wrong?

What if A1 = A2 and P(A1) = 1/2?

And what does A+B mean for sets A and B? And what does /A mean?
 


I don't have the original statements, but we were looking for a counterexample. The last one instead of plus is union and / is complement. I am sure that one is false too.
 


kezman said:
I don't have the original statements, but we were looking for a counterexample. The last one instead of plus is union and / is complement. I am sure that one is false too.

Me too.
 


kezman said:
but we were looking for a counterexample.
So that means you are trying to disprove them. It would have been useful if you had of stated that at the outset.
 


kezman said:
1) A1 A2 be two events, show that ... etc.

Are Venn diagrams good enough for demonstrating this?[/color]
 


thanks everybody for the help. At the beginning we didnt know if there were ok or not. Now we are sure. thanks
 

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