I toss two coins and look at the outcome. I then tell you that at least one of the coins is showing up as "tails". What is the chance that the other one is showing "tails" as well?

(from techInterview.org)

(In reply to re: Solution Using Real Prob/Stats by SilverKnight)

ell- first let me say i did read the solution, what i think you might be missing is that HT and TH are functionally equivilant, meaning that there are 2 not 3 outcomes even in art's solution - i.e. 1/2 not 1/3 but anyway...

On Independence-

In this particular example the probability of a particular outcome (which we will call flip one or F1), that is to say H or T, does not change the probability of the outcome of F2 (flip 2).
i.e. when P(F1)>0, P(F1|F2) = P(F2)
indicating independence
Furthermore- the multiplication rule here become

P(F1 intersect F2)=P(F1)P(F2|F1)=P(F1)P(F2)
Which implies that when P(F2)>0, then

P(F1|F2)= (P(F1 intersect F2)/P(F2)) = (P(F1)P(F2))/P(F2)= P(F1)


Now- I am going to stop here before i get to far into a Statistics Class, if you want me to follow up and complete this explanation let me know what you made of this begining so I know where you are coming from on a mathematics level-

Posted by Eberhard on 2003-12-03 14:20:58