Proving Statements: A Guide to Help You Out

[Altemicione]

1. Prove each of the following statements (assume that any conditioning event has positive probability).
(a) If A is subset of B then P(B|A)=1 and p(A|B)=P(A)/P(B).
(b) If A and B are mutually exclusive, then p(A|A u B)=((P(A)/((P(A)+P
(B))
(C) P(A n B n C)= P(A|B n C) P( B|C) P(C)

I"m really having problem in doing these. could someone help me out?

 

[matt grime]

You just need to use the rules/identities of probability:

P(X|Y) = P(XnY)/P(Y)

and if A < B, then P(AnB)= P(A) since AnB=A, and P(AuB)=P(B) since AuB=B

if A and B are mutually exclusive then P(AnB)=0 and P(AuB)=P(A)+P(B)

the third follows from repeatedly applying the formula for conditional probability.

 

[Wong]

Moderator's note: please don't do others' homework for them

 

[Hurkyl]

Have you been able to get anywhere on this, Altemicione?

 

[supundika]

Moderator's note: Same goes for you

 

[Jin314159]

Why can't we help a brother out?

 

[matt grime]

you can, but just feeding the answers helps no one.

 

[Tom McCurdy]

helps him pass his class
so it helps one person
then it helps his parents so they have to pay less for when he goes to college if he is still in high school
so then the fincacial benefits spread through is family
so in the end it could help a lot of people

plus he prob learn how to do in class tomorrow
but if u dont' have homework u get 0

 

[Gokul43201]

You think feeding him homework solutions makes him a better student and improves his odds of scoring higher in SATs (or whatever) ?

 

[humanino]

"If someone is hungry, don't give him a fish : teach him to fish !"
who said that ?

 

[matt grime]

Probably Gandhi

 

[HallsofIvy]

"If you give a man a fish, he will eat for a day. If you teach a man to fish, he will never work another day in his life!"

 

[Galileo]

"If you give a man a fish, he will eat for a day. If you teach a man to fish, he will never work another day in his life!"

Or:

If you give a man a fish he will eat for a day. If you teach a man to fish he will drink beer, tell lies and wear a stupid hat.

 

[humanino]

Thanks you all for answering my "off-topic" question ! (although Galileo's version looks suspicous to me (^_^)

 

[Gokul43201]

...although Galileo's version looks suspicous to me...

You mean 'fishy' ?

 

[humanino]

Sorry, I am not too sure about what fishy could mean ...