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

[kezman]

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

 

[LCKurtz]

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?

 

[kezman]

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.

 

[LCKurtz]

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.

 

[uart]

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.

 

[NascentOxygen]

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

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

 

[kezman]

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