DSE 2004. part 2

[Mauli]

 
q2(A)
http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/26_jun_2004_option_a.pdf.
I REALLY HAVE NO CLUE HOW TO DO THIS.
someone please help.

[Sinistral]

are u talking about that "loser" game question?

a) loser is decided in the very first game ==> exactly one gets a head or exactly one gets a tail.
P(finding a loser)= nC1pq^n-1 + nC1qp^n-1  where q=1-p

b)
P(not finding a loser)= no exact 1 head OR no exact 1 tail.
                            = 1 - nC1pq^n-1  + 1 - nC1qp^n-1
                            = 2 - nC1pq^n-1  - nC1qp^n-1
P(finding a loser in kth trial)= P(no loser till k-1  trials and a loser in kth trial)
                                     =  {[2 - nC1pq^n-1  - nC1qp^n-1]^(k-1)} * {nC1pq^n-1 + nC1qp^n-1}

I hope i didnt miss anything.