Right, this is probably wrong but I don't know much about stats.
I'm playing a game where when you win you get to spin a wheel that is split into 10, all equally likely to be landed on. After you spin the wheel you get the reward on that segment. The next time you win you spin the same wheel but 9 parts have a reward and if you land on the 10th you get no reward.
I'm trying to figure out the average number of spins needed to win every prize on the wheel.
First spin you always get a prize.
To get the second prize
(9/10) 1 spin, [1/10][9/10] 2 spins, [1/10]^2 [9/10] 3 spins, etc
Third prize
(8/10) 1 spin, [2/10][8/10] 2 spins, [2/10]^2 [8/10]3 spins, etc
First of all is that correct? I'm pretty sure it is.
Then does it work if I calculate what all of those sequences converge to individually & then add them all together?
So first prize is 1 spin, second prize is 1.1 recurring spins so on average I'd need 2.1 recurring spins to win two prizes?
If this is nonsense which wouldn't surprise me how do I go about doing it? If it's not nonsense is there a better way of doing it?
The number is spat out on n=1 to 10000 seem realistic.
I work out I need ~29.3 spins so I'd round that up and say 30?
If this has worked can I work out the variance just by summing each individual variance and adding them? I think I remember that sometimes this works and sometimes it doesn't and it seems to me this is relatively simple distributions so would work? (If not I don't need an answer explaining why)
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