705 karma · joined March 31, 2022
1/10 odds, 10 entrants, one winner expected on average.
Given a particular winner: Expect: 0.9 + 1 winners
Given the same particular loser: Expect: 0.9 winners
Over all cases we see: 0.1(1.9) + 0.9(0.9) = 1 winners
Checks out, but if the numbers are correct then any winner should be able to calculate the higher average and be right knowing only that there is at least one winner. So in cases where there is at least one winner: P(winners>=1)=1-(9/10)^10=~65% The expectation should work out to 1.9. The rest of the time we expect zero winners. However if I use those numbers I get an overall expected number of winners as 1.237, which has increased the overall number of winners across all cases. In order for that number to work out to one, the expected winners when there is at least one winner would have to be ~1.535. Which suggests that the expected outcome is different depending on if you check your own ticket, or someone else's, even if you see the same thing?
Am I just not on for math today? I thought the solution to the paradox would be that the higher expectation discounts outcomes with zero winners.
I think this is a good hint that the conclusion isn't true. Just think about what it would mean if this were true for a sample of lotto winners. For a winner, if they win, their average number of winners is higher than the global average. Repeat this logic for each individual winner... And every winner wins with a higher number of winners than the average. Which is clearly impossible.
It would be true if you were guaranteed to win, since that's the assumption you have conditioned the probability on, but that's not a lottery then. If you want to get the actual expected value across all samples you need to take a weighted sum including the expected value when you don't win.
Society requires effort and investment that doesn't produce immediate material benefits. Rationalizing everything down to profit and loss encourages people to see the collected effort as a tragedy of the commons. You need to actually want to be part of a society to start, then if enough people join you, you can actually build one!
In my opinion the best teachers just direct your questions in the direction where the answers you find give you the most useful information. I'm optimistic that AI could be an improvement to the average for scientifically minded learners, though I wouldn't expect it to be more effective than a 1 on 1 with a good teacher.
"->Should do ... ->Or ... Throughout the week."
Not sure why they worded it that way, maybe adults with busy schedules engage less with _ per day than _ per week recommendations.
That being said, it's all a function of how much light enters your eye. You can look up the exposure limits of the human retina for different frequencies of light to get an idea how little is actually required to damage your eye. The target or sensor should be sensitive enough to react to that much incident light. Just putting something behind the glasses and have it not get cut is definitely not enough to indicate no eye damage.
Either way, the details page[1] supports all of my above points. It even comments on the page how rare it is to find a suitable site like the one they've chosen.