# Probability prop.

• July 27th 2011, 02:57 PM
kezman
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
• July 28th 2011, 02:05 PM
awkward
Re: Probability prop.
1) isn't true. Are you sure you have copied the exercise correctly?
• July 28th 2011, 03:24 PM
Plato
Re: Probability prop.
Quote:

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 $\mathcal{P}(A_1),~\mathcal{P}(A_2),~\&~\mathcal{P} (A_1\cap A_2)~?$
• July 28th 2011, 05:45 PM
kezman
Re: Probability prop.
Quote:

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