(1). The person who starts wins in the following sequences (with the probability of occurring given in brackets)

H (1/2)

TTH (1/8)

TTTTH (1/32)

TTTTTTH (1/128)

TTTTTTTTH (1/512)

Therefore total probability of winning

= (256 + 64 + 16 + 4 + 1)/512

= 341/512

(2) The chance of a draw is in the sequence

TTTTTTTTTT (1/1024)

Since the starter's chance of a win + starter's chance of a draw + starter's chance of a defeat = 1,

341/512 + 1/1024 + starter's chance of a defeat = 1

or 683/1024 + starter's chance of a defeat = 1

=> starter's chance of a defeat = 341/1024

The odds of defeat of the starter is therefore, 341 to 683.

Hope that helps.

P.S. theArch, now I see your "reasoning" (I wasn't logged in when I saw your post). Phew !! Did you use AutoCad to draw that one??

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