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But what I said earlier is still right – at the final step the cumulative probability of no match is the same as 1 minus the cumulative probability of at least one match. It’s just that to do the iterations you have to multiply the probabilty of no match at successive steps rather than adding the possibility of match (which quickly and wrongly gets you over 100%).
Arkady, yeah, once you get up to 30 and keep multipling the likelihood of no match at each step by the cumulative likelihood of no match at the next step.
im also angry right now. i was charged for an expensive tomato when i bought the cheapest one. grrrr. i bought the tomatos that were like 1.49 per pound (think it’s per pound) but was charged for the kind that were 2.99 per pound!!! the thing is ive always wondered how they can tell what kind of tomato it is when it’s wrapped in a plastic bag? grrrr
*rob*
It was explained to me by a WW 2 Naval Flying Ace when he was also talking about the probability of returning from a bombing sortie. In theory each flight was a single event w/ the same risk each time but obviously there were variables; inexperience in a tyro for instance. But the fly boys were certain that they were not playing odds the more flights they flew a la likelihood of a run of “heads” when flipping coins.
my best friend who killed hersef in 01 was feb 9th (im feb 9th), two people at work (of about 30) share my birthday. but i think it’s more an aquarian cluster than any kind of mathematics involved.
*rob*
Lech – As I recall, it’s roughly 30/70 – i.e. 30% unlikely that 2 people will share the date & 70% likely.
quote:
Apparently there are people in the world who are upset that Bloomberg drinks his beer over ice.
in the summer i pour 40’s over ice sometimes. i had no idea this is soo… frowned upon? i mean i guess if you are drinking expensive beer maybe i can see that putting it over ice might not be as good, but for most beer, who cares? i saw that post over on gothamist. a bunch of cheesy ass moonface artisinal beer drinkers had a shit fit. typical, i guess. these people must be rebelling against their PBR roots, just like they moved to nyc to rebel against their midwestern suburban roots.
I drank my beer on ice in Ho Chi Minh City when I was there in the early 90s. My friend whom I was there with would not take the ice the first day to see if I got sick. We went back to the little restaurant the next day and they were out in front breaking up th ice on the sidewalk!!!!!!!!
I never got sick and took the ice every day.
365 days.
So each person in any given group has a 1/365 chance of having a birthday on any particular day. And the chance that any other person has the same birthday is the number of other people over 365 (obviously capped at 100%).
So let’s say you are adding people to the group 1 by 1, like in my roulette wheel example. Take person 10. He has a 1/365 chance of having a b-day on any particular day, and the chance of one of the other 9 people having a b-day on any particular day is 9/365. Yeah that’s right. So the probability of there being a “match” on any particular day is 9/365, and the total probability of person 10 having the same birthday as one of the other 9 people is (1/365*9/365)*365…. or 2.47%….. sounds OK so far.
So then how do you add up the cumulative probability for the other 9 people matching each other. Obviously it’s not just 2.47% x 10, because that’s double counting 10’s probability vis-a-vis the first 9. No I think you do what we just did for 10 for each of 1 through 9. But then you can’t just add up the individual probabilities of each of 1 through 10….. because by the time you get to 365 you would have way more than 100%, which can’t be right. Somehow you have to figure out how to add up the individual probabilities.
hermmmm…… no, that’s all just fucking wrong. It doesn’t add up like that dumbass. it’s what Arkady said. It’s about the probability of not hitting, not the probability of hitting.
Sooooo….. The probability of 10 NOT hitting is 97.53%. Hey not we’re on to something. (thanks Arkady). right, right, right…. So you take the first guy’s probability of not hitting, multiply it by the second guy, etc., and then take the inverse of it to get the probability that there has NOT been a match…..
I think that sounds right.
So…..
Guy 1: 0% chance of match, 100% chance of no match.
Guy 2: 1/365 chance of match, 99.73% chance no match.
Guy 3: (1/365*2/365)*365 chance of match, or .55%, so 99.45% chance of no match. So there was a 99.73% chance of getting this step without a match, and a 99.45% chance of getting to the next step without a match, so you multiply those by each other and….99.27% cumulative chance of no match.
Guy 4: (1/365*3/365)*365, or .82% chance of match, so 99.18% chance of no match, multiply that by the cumulative chance of no match at the last step that’s a cumulative probability of 98.46% that there is no match by this step.
And so on and so on…. until when you get to 365 there is just a 100% chance of match at that step.
I think that sounds right. Anyone disagree?
Goddamit I’m procrastinating. I need to get back to work.