A happy winner of this Sunday’s Free PCB giveaway suggests there is a 50% chance of winning a PCB after 25 weeks:
Thanks a lot! Just for the statistics: it took 13 drawings to get this code, which is way below average (there seem to be, on average, 110 comments on each sunday, which means it takes 25 weeks for a 50% chance :)
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Am I missing something here? If probability of winning is p = 1/110 or just under 1%, let q equal chance of losing,
q = 1-p or just over 99% chance of losing.
The chance of losing n weeks in a row is q^n, so chance of winning once (or more) is 1-q^n.
The if the 50% breakpoint is chosen, then
q^n = 0.5 (chance of losing n times in a row to reach 50%)
Take log of both sides
log(q^n) = n log(q) = log(0.5)
Solving for n,
n = log(0.5)/log(q) = 75.9 weeks.
You can check that q^75.9 is very close to 50%.
Yes, I am still trying.
Thank you for an alternate perspective, it’s really cool :)
Probability of winning is p = 2/110 though, I think, because we give away 2 each week.
I did not realize you gave away two. In that case, the 50% point comes at 37.8 weeks.