1. ## Probability prop.

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 dont know if I copied them wrong.
thanks

2. ## Re: Probability prop.

1) isn't true. Are you sure you have copied the exercise correctly?

3. ## Re: Probability prop.

Originally Posted by kezman
1) A1 A2 be two events, show that P (A1 ∩ A2) ≤ P (A1) . P (A2)
This false. Consider the set $\mathbb{D}=\{0,1,2,3,4,5,6,7,8,9\}$
Pick one of those digits at random.
Let $A_1$ be the event "that digit is prime".
Let $A_2$ be the event "that digit is odd".

What are $\mathcal{P}(A_1),~\mathcal{P}(A_2),~\&~\mathcal{P} (A_1\cap A_2)~?$

4. ## Re: Probability prop.

Originally Posted by Plato
This false. Consider the set $\mathbb{D}=\{0,1,2,3,4,5,6,7,8,9\}$
Pick one of those digits at random.
Let $A_1$ be the event "that digit is prime".
Let $A_2$ be the event "that digit is odd".

What are $\mathcal{P}(A_1),~\mathcal{P}(A_2),~\&~\mathcal{P} (A_1\cap A_2)~?$
1/2*4/10<3/10
4/20<3/10
2/10<3/10

thanks plato