by **Alex.vollenga** » Wed Jul 26, 2017 6:37 am

I am thinking that in all sequences of outcomes of n people, the last outcome is always H. We have for example TTTH or TTH or H.

For the number of H to be > number of T, we must have the following;

We must have a good number of H in the first toss (probability 1/2) and for the rest of sequences, the total number of T must be less than the total number of H at the first toss. For example, H, H, TH, TTH, H, H, TH, TH, TTTH.

The total probability must be 1/[tex]2^{p1}[/tex]+1/[tex]2^{p2}[/tex]+...+1/[tex]2^{pn}[/tex] where p1+p2+...+pn=2k+1 (the total number of tosses) and there must be P(total probability)>1/2.

We also have that the total number of HEADS is n (since each player stops tossing once he gets a H), so it must be n>(2k+1)/2.

How do we calculate the required probability?