probabilities

[donys]

Hi again...This is my last question for today.

I know that i send a lot of threads but...i dont have anyone else to help me.

 

Most of the times i dont send any solutions.I try but sometimes i dont understand and so...i dont have something to write.I post frequently

because if i dont give a 50% of correct answers i will not have the chance to write in the final exams...its a stupid rule.

 

My last 2 questions for today are.

 

1.We must prove that if P(A/B)=1 then P(B compl. / A compl.)=1

i wrote a lot of things but ..i didnt prove nothing : ~)

 

2.A and B are two events with non zero probabilities.

I must show (prove) if the following are i)correct,ii)faulse iii)correct under some conventions.

a)if A and B are foreign then they are independent (i dont know if this is the correct word) butif they are foreign P(A[intersect]B)=[empty-set]

b)if A and B are independent then they are foreign

c)P(A)=P(B)=0.6 A,B are foreign

c)P(A)=P(B)=0.6 A,B are independent

[MandrakeRoot]

What do you mean with foreign ?

Don't you mean disjoint ?

 

What have you tried for the first exercise for example ?

 

Mandrake

[MandrakeRoot]

Let me do one for you => 2c

Assuming that with foreign you mean disjoint;

assuming A and B are disjoint and P(A)=P(B) > 1/2. Their union is surely contained in the set of all events Omega and since they are disjoint we can write

P(Omega) >= P(A union B) = P(A) + P(B) > 1, which is a contradiction. Hence when P(A)=P(B) > 1/2, the two sets cannot be disjoint and must have common compoments. Even : P(A intersection B) > 0 ! (try understanding why)

 

Mandrake