I have this question as a Homework from my probabilty class..I have hard time thinkin over and over abt this q..can smby. pls help!!This is due on monday..

Consider two independent tosses of a fair coin.Let A be the event that the first toss lands heads, Let B be the event that the second toss lands heads, and let C be the event that the both land on the sam side. show that the events A, B, C are pairwise independent but not independent.

this Q from conditional probability and independece chapter..
thanks a lot for the help...

NO..

The Q doesn't define any sides for C...that's where i'm gettin confused..do we have assume that C could be the event that both lands on tail as well..

The Question is complete as it excatly taken out of the book ..word for word..

In my point of view, we have to make consideration for both headsa n tails ..as we have to prove pairwise independent..the fact that no ther numbers are give, i think we have to consider other independet assumptions to get to the solution..

Well, "C: the probability (A intersection B) = probability of A . probability of B (mutually exclusive events)" which i agree but you can't assume this :" I have taken let P(A) be the event that coin 1 lands on heads or tails...and P(B) lands on heads or tails" as the Q specifically tells that A lands on head and B lands on tail...

And what do I have to show which makes A, B,C pairwise independet ?


Like If I show the below condition, then I can say they are independent..
P(A)= E1, P(B)= E2, P(C)= E3
P(E1E2E3) =P(E1) P(E2) P(E3) & ( Intersection of E1E2E3)
P(E1E2)=P(E1)P(E2)&
P(E1E3)=P(E1)P(E3)&
P(E2E3)=P(E2)P(E3)

thanks....

MeMySelfNepal1,

You seem to be good in probability. I did not go thru your solution .I am bad at math either but not going solve it.Here is a question for you.
What is the probability that Monarchy will stay in Nepal ?:)..Give a serious thought .It is just not simple question!!!!

I actually photocopy the whole book, as it was too expensive to buy ..
the name of the book is A first course in Probability..by Seldon Rose-Prentice Hall

Beleive me this Q is not simple as it sounds..this Q has been asked in Actuarial P Exam..
I tried using conditional probabilty and using compliment of event C but i seem to go nowhere....

The probabulity that king will stay is flat out 0.0000000000000000000001,
but the conditional probability that king will stay given that the Girija will live another 1 yr, is 1/10. , which is irrevelant cauz the probability that Girija live for another 1 yr is 1/1000000000000. ... ...

Time will tell who is poor abt. the king...will not take that long..that's for sure...
"....Do not worry about Monarchy, it's staying there for the protection of Nepalis.."

tell him to protect his son's A##.., I really think we should put him on the jail for killing all those innocent ppls...Don't get me wrong, Maosists should be held responsible for their action too.. and so does all those corrupt Netas who made the mockery out of wounderful system of "Democracy" to fill their pockets...............