↳
1/3
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1/3 Because if he requires 2 heads = $2, then it means he require HH out of {HH,HT ,TH,TT} We cannot consider TT because it would turn to zero. Therefore, he has 1 chance out of 3. Hence 1/3. Less
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Marchov chain with 2 and -1 absorbing OR geometric series 1/4^n from 1 to inf=1/3 Less
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It took me a while to get the correct answer which is 7 races.