I toss a coin repeatedly. The coin is unfair and P(H)=1/3. The game ends the first time that two consecutive heads (HH) or two consecuative tails (TT) are observed. I win if the HH is observed and i lose if the TT is observed. For example, if the outcome is HTHTT, i lose. On the other hand, if the outcome is THTHTHH, i win. Find the probability that i win

7/28.........................however, the number of tosses is not well defined. If there is no limit to the number of tosses, you could go even ten tosses without winning or losing.......................you may clarify please!!

Can you explain how you got the 7/23? (i will tip you for this so its not a waste of your time) And i wish i could clarify more but that is the entire question and all the info i have

okay...a coin is unfair such the chances of getting head are limited to 1/3 instead of the usual 1/2. i took the first 4 tosses of the coin, so here is the outcome;

1/3 getting the first head, then the other 1/3 for subsequent head.(we close at that point since the outcome is HH)..............................(1/3x1/3)=1/9

still when we get the first head(1/3) we may land on the T the next toss,then on the third toss we get two heads............................(1/3x2/3x1/3x1/3)=2/81

.........................does this look impress dear....hope you're getting before we conclude...you there?