Please feel free to critique the maths but I also really want a Gwen Doll and no one is selling so I took a shot at the probability distribution function:
The chance of getting a Gwen Doll, g is 0.05% (0.0005) therefore chance of not getting one (1-g) is 99.95% (0.9995).
The chance of not getting any Gwen Dolls from n presents is just the chance of not getting one to the power of n => (1-g)^n. (not scoring, not scoring, not scoring ... me trying to pull women on a series of endless Friday nights out)
The chance of getting anything else (i.e. getting anything other than nothing => one or more dolls) is just 1-(1-g)^n. (He scores and it could (only in theory) even be a threesome)
If you want to know how many presents you'd have to open for a certain chance of a Gwen Doll, say I'd like to be 5/6 sure of getting a doll then.
1-(1-g)^n = 5/6 => 1-5/6= (1-g)^n => n log(1-g) = log(1/6) => n = log(1/6) / log(1-g)
So, if any of this is correct, in order to be (on average) certain (does that even make sense?!) to the extent of 5/6 of at least one Gwen Doll we'd want to open 3,582 presents and there is still a 1/6 of not getting one.
It's a crapshoot and a rich man's game. Might power up Visual Basic later and run a quick simulator to just test out the above. I'm bound to have got it wrong somewhere along the way.
