Strange and/or funny quote 272
| [14:56] <+Darvince> i want to know [14:56] <+Darvince> the chances of winning the powerball [14:56] <+Darvince> if you bought 292201338 tickets [14:56] <+Darvince> which is the odds of winning [14:56] <+Kalassak> probably about half [14:57] <+Darvince> um [14:57] <+Darvince> that seems really high [14:57] <+Kalassak> actually idk [14:57] <+Kalassak> imagine for example [14:57] <+Kalassak> flipping a coin [14:58] <+Kalassak> you have a 1/2 chance of winning the "lottery" [14:58] <+Darvince> well you can get the same ticket twice [14:58] <+Darvince> so [14:58] <+Darvince> it is flipping a 292201338-sided coin basically [14:58] <+Kalassak> you could write a program to fill out a bunch of sheets [14:58] <+Kalassak> so that you actually got all of them [14:58] <+Kalassak> i guess [14:59] <+Darvince> oh yeah [15:00] <+Darvince> the powerball is choose your own number [15:00] <+Darvince> but let's imagine the numbers you're choosing are entirely random [15:00] <+Kalassak> ok [15:00] <+Kalassak> so imagine [15:00] <+Kalassak> a lottery in which a coin is flipped [15:00] <+Kalassak> and you choose to quick pick [15:00] <+Kalassak> basically [15:00] <+Kalassak> flip your own coin [15:01] <+Kalassak> the chance that they will match is 1/2 [15:01] <+Darvince> would the chance of winning be 1/((292201337/292201338)*292201338) ? [15:01] <+Kalassak> but you allow the quick pick to randomly select [15:01] <+Kalassak> so you flip it again to buy another ticket [15:01] <+Kalassak> your chance of winning is what [15:01] <+Kalassak> 3/4? [15:01] <+Darvince> woops it should be to the x [15:01] <+Kalassak> because there is a 25% chance that you will only flip two tails [15:01] <+Kalassak> er [15:01] <+Kalassak> wahtever the winning thing isn't [15:01] <+Darvince> i got something awfully close to e [15:02] <+Darvince> wth [15:02] <+Kalassak> let's just assume heads wins [15:03] <+Kalassak> your chance is like [15:03] <+Darvince> it would appear [15:03] <+Darvince> the horizontal asymptote [15:03] <+Kalassak> 1 - 1/292201338^2 [15:03] <+Darvince> for 1/(((x-1)/x)^x) is e [15:03] <+Kalassak> right [15:03] <+Kalassak> ? [15:03] <+Darvince> yes [15:03] <+Kalassak> which is basically 100% [15:03] <+Kalassak> that seems wrong [15:04] <+Darvince> try 292201337/292201338 [15:04] <+Darvince> if you can choose the number for a powerball ticket [15:04] <+Darvince> then you could have a 100% chance of winning by buying 69^5*12 tickets [15:04] <+Darvince> or 69^5*26 [15:04] <+Darvince> i forget [15:05] <+Kalassak> ok let's extend this [15:05] <+Kalassak> imagine you have to match two coins [15:05] <+Kalassak> and say the winning thing is heads heads [15:06] <+Kalassak> you have a 1/4 chance of winning each time [15:06] <+Darvince> does order matter [15:06] <+Darvince> in the powerball [15:06] <+Darvince> oh god [15:06] <+Kalassak> no [15:06] <+Yqt1001> if it did the odds would be ridiculous lmao [15:06] <+Darvince> it must not because 69^5 is larger than 292 million [15:07] <+Yqt1001> that's not how you do combinations [15:07] <+Yqt1001> combinations deal with factorial [15:07] <+Darvince> oh god [15:07] <+Darvince> that thing i learned last year [15:07] <+Darvince> that i forgot [15:07] <+Kalassak> ok so if you did it twice then [15:08] <+Darvince> «five white balls are drawn from a drum with 69 balls and one red ball is drawn from a drum with 26 balls.» [15:08] <+Darvince> oh [15:08] <+Darvince> so [15:08] <+Darvince> 69!/5!*26 [15:08] <+Darvince> ? [15:08] <+Kalassak> >69 [15:08] <+Kalassak> i wonder [15:08] <+Kalassak> if they did that because [15:08] <+Kalassak> most calculators [15:08] <+Kalassak> 70! is overflow [15:09] <+Darvince> it increased last year some time [15:09] <+Kalassak> probably not [15:09] <+Yqt1001> that seems pretty legit [15:12] <+Darvince> yqt1001 what would the equation be [15:12] <+Yqt1001> you're close enough for my liking [15:12] <+Yqt1001> I can't remember it's been too long :P [15:14] <+Kalassak> yqt pls send to help [15:14] <+Yqt1001> what [15:14] <+Kalassak> how do you find the probability of getting heads after n flips of a coin [15:14] <+Yqt1001> 2^n [15:14] <+Kalassak> how about [15:14] <+Kalassak> 2 heads after n flips of 2 coins [15:14] <+Yqt1001> well [15:15] <+Yqt1001> kalassak [15:15] <+Yqt1001> if the first question is worded as "the sequence of h/t that leads you to that flip of heads" then it's 2^n [15:15] <+Yqt1001> but getting heads after n flips of a coin is 1/2 [15:16] <+Kalassak> that doesn't make sense like what if i replace n with something [15:16] <+Kalassak> "how do you find the probability of getting heads after 10 flips of a coin" [15:16] <+Kalassak> you just told me that [15:16] <+Kalassak> if i flip the coin 10 times [15:16] <+Kalassak> i have a 50% of getting heads [15:16] <+Yqt1001> the 10th time yes [15:16] <+Kalassak> not on the 10th flip [15:16] <+Kalassak> after 10 flips! [15:16] <+Kalassak> all 10 flips [15:16] <+blotz> hmm [15:16] <+Yqt1001> then its 2^10 [15:16] <+Kalassak> during [15:17] <+Kalassak> waht does that mean [15:17] <+Kalassak> 1024 [15:17] <+Kalassak> 102400% of the time [15:17] <+Kalassak> i will get heads [15:17] <+Yqt1001> no the odds are 1024:1 [15:17] <+Kalassak> ok [15:17] <+BlaBla44> You mean the probability of getting 10 heads if you toss 10 coins? [15:17] <+Kalassak> no bla [15:18] <+Kalassak> getting at least one heads [15:18] <+Kalassak> with 10 flips [15:18] <+blotz> oh [15:18] <+Yqt1001> what now you're changing everything [15:18] <+Kalassak> no this is the same thing [15:18] <+blotz> those are independent variables so [15:18] <+Kalassak> !!!! [15:18] <+Yqt1001> no the odds of that are the odds of some combination of 10 heads no tails [15:18] <+Yqt1001> 9 heads one tails [15:18] <+blotz> oh kal the 1st one i thoguht you meant flipping 10 coins and then getting heads [15:18] <+blotz> i was confused [15:18] <+Yqt1001> on and one until 1 head 9 tails [15:18] <+Kalassak> this is some cheese [15:18] <+Kalassak> ok so imagine [15:18] <+Kalassak> a lottery [15:18] <+Kalassak> with only two numbers [15:19] <+Kalassak> 1 and 2 or 0 and 1 i don't care [15:19] <+Kalassak> what is the chance of winning [15:19] <+Kalassak> if i buy [15:19] <+Kalassak> x tickets [15:19] <+Kalassak> using quick pick [15:19] <+Yqt1001> 1/2 [15:19] <+Kalassak> so 50% for 1 [15:19] <+Kalassak> ?% for 2 [15:19] <+Kalassak> ?% for 3 [15:19] <+blotz> 75% [15:19] <+Kalassak> etc [15:19] <+blotz> for 2 [15:19] <+Yqt1001> 1/2 for one, then you add 1/2 [15:19] <+Yqt1001> until you get x tickets [15:19] <+Kalassak> add 1/2 of what [15:19] <+BlaBla44> There are 1024 ways to toss 10 coins. 1023 of them have at least 1 heads. So the probability is 1023/1024 [15:20] <+blotz> 75% chance of getting heads in 2 flips [15:20] <+Kalassak> because it's not 100% [15:20] <+blotz> yeah [15:20] <+Kalassak> and it's not 50% at 2 tickets either [15:20] <+blotz> what bla said [15:20] <+Yqt1001> multiply it by 1.5 [15:20] <+Darvince> 1/2 of 1/2 [15:20] <+Kalassak> ok so that's simple [15:20] <+Kalassak> it's [15:20] <+Kalassak> 1 - 1/2^n [15:20] <+Darvince> so how do we generalize this [15:20] <+Kalassak> but what if you do the same thing [15:20] <+Kalassak> with m coins [15:20] <+Kalassak> what i'm trying to get to [15:21] <+BlaBla44> There's a generalization in my book on statistical physics I think [15:21] <+Yqt1001> statistical physics [15:22] <+Kalassak> is what is the probability of winning when buying n tickets for a lottery of m coins which have s sides [15:22] <+Kalassak> coins/dice/numbers whatever you want [15:22] <+blotz> wait what [15:22] <+blotz> so [15:22] <+blotz> every ticket [15:22] <+blotz> you get a coin [15:22] <+BlaBla44> The first day we met our lecturer he tried to convince us he could predict coin tosses by calculating Newton's laws in his head when tossing them [15:22] <+blotz> for a die? wat [15:22] <+Kalassak> blotz just replace n m and s with numbers [15:22] <+Kalassak> for example [15:23] <+blotz> buy 1 ticket of 10 die with 5 sides [15:23] <+blotz> oh [15:23] <+Kalassak> "what is the probability of winning when buying 100 tickets for a lottery of 5 coins which have 69 sides" [15:23] <+Kalassak> aka [15:23] <+Kalassak> the powerball without the powerball [15:25] <+Yqt1001> strange [15:25] <+Yqt1001> I don't see how someone's knowledge can really change the result of a coin flip [15:26] <+Yqt1001> unless the person flipping it knows how to throw it consistently [15:26] <+blotz> oh [15:27] <+blotz> well [15:27] <+Kalassak> yqt waht is the probability of winning a lottery after buying n tickets for a lottery with 2 numbers that go from 1-2 [15:27] <+BlaBla44> Nono, it doesn't change the result of the coin flip. But imagine you know the coin has 2 sides. From your knowledge, the probability of getting heads is then 50%. But if you know it has either 2 or 3 sides, with 1 side being heads... Then if you have no idea if it's 2 or 3 sides, you'll assume 50% chance of either. So if it has 2 sides, 50% chance, 3 sides, 33% chance, giving 0.5*0.5 + 0.5*0.33 = 41.5% chance of heads. [15:27] <+blotz> @kal, P=n/m*s [15:27] <+blotz> right [15:27] <+blotz> idk [15:28] <+Yqt1001> oh I see [15:28] <+blotz> like [15:28] <+blotz> possibilites are m * s [15:28] <+Yqt1001> probability is like quantum mechanics, when dealing with uncertainties it's better just to ignore it [15:28] <+BlaBla44> Kol [15:28] <+Kalassak> blotz that doesn't work [15:28] <+blotz> gg [15:29] <+Kalassak> 2 tickets/1 coin*2 sides [15:29] <+Kalassak> = 1 [15:29] <+blotz> oh [15:29] <+blotz> right [15:29] <+blotz> well [15:29] <+blotz> if the tickets are uniqe [15:29] <+blotz> it works [15:29] <+blotz> like [15:29] <+Kalassak> yes [15:29] <+blotz> who would buy heads twice [15:30] <+Kalassak> win double the money tbh [15:30] <+Darvince> i think the powerball is such that each ball must be different [15:30] <+blotz> ok so it's just less [15:30] <+blotz> so [15:30] <+blotz> so [15:30] <+blotz> idk [15:36] <+Darvince> so whjat is the generalization [15:39] <+Kalassak> no one knows [15:39] <+Kalassak> statistics is too hard for human beings it seems [15:41] <+TheFedBla> You mean n tosses of coins and m heads and n-m tails? [15:41] <+TheFedBla> The binomial distribution I think [15:41] <+Kalassak> is what is the probability of winning when buying n tickets for a lottery of m coins which have s sides [15:42] <+Kalassak> imagine the coins can be non-coins [15:42] <+Kalassak> like [15:42] <+Kalassak> balls with numbers on them [15:42] <+Kalassak> or dice [15:42] <+Darvince> also [15:42] <+Darvince> you cannot draw a coin with the same side [15:43] <+TheFedBla> the general solution is not to participate in the lottery, because lotteries always have the statistics in their favor [15:43] <+Darvince> oh my god [15:43] <+Kalassak> well of course [15:43] <+Darvince> -_- [15:43] <+Kalassak> but [15:43] <+Kalassak> do we have $400 million [15:43] <+Kalassak> to spend on lottery tickets [15:43] <+Darvince> i want to know the answer for the probability [15:43] <+Darvince> not [15:43] <+Darvince> what i should do about the lottery [15:44] <+Kalassak> i think what bla means is [15:44] <+Kalassak> "i don't have time to figure it out" [15:44] <+TheFedBla> ^ [15:45] <+Kalassak> how sad [15:45] <+Kalassak> you should buy a 24th hour [15:45] <+Kalassak> er [15:45] <+Kalassak> 25th hour [15:48] <+TheFedBla> My lecturer in mathematics for physicists described lotteries as a tax on stupidity [15:48] <+TheFedBla> kol [15:49] <+Darvince> ok [15:49] <+Darvince> micamo provided me with the answer [15:49] <+Darvince> time to figure it out [15:49] <+Kalassak> wow micamo [15:50] <+Kalassak> wut was it [15:51] <+Darvince> n/s^m for ones where it can be the same [15:51] <+Darvince> nm!(s-m)!/s! for ones where it cannot [15:51] <+Kalassak> ah [15:52] <+Kalassak> syule [15:57] <+Darvince> i got complex infinity [16:21] <+Darvince> https://www.reddit.com/r/learnmath/ kalassak should i ask here [16:22] <+Kalassak> sure [16:22] <+Kalassak> or [16:22] <+Kalassak> r/theydidthemath/ [16:22] <+Kalassak> or w/e it's called [16:32] <syule> darvince ask what [16:33] <+Darvince> what is the chance of winning the powerball by buying 292201338 random tickets [16:33] <syule> hm [16:34] <syule> and the chance if you buy one random ticket is 1/that quantity? [16:34] <+Darvince> yes [16:34] <syule> 1/292201338 [16:34] <syule> ok [16:34] <+Darvince> but idk what the chance is if you buy two random tickets [16:34] <+Darvince> it's very close to 2/292201338 but very slightly less [16:34] <+Darvince> my first guess is that it would be 292201337/292201338^292201338 [16:34] <syule> it's 1-1/e [16:35] <syule> i pulled that from memory so let me see if i did that right [16:35] <+Darvince> FINALLY [16:35] <+Darvince> AN ANSWER [16:35] <+Darvince> WEW [16:35] <syule> yeah it should be right [16:35] <+Darvince> i have been waiting [16:35] <+Darvince> literally all day [16:35] <+Darvince> for an answer [16:35] <+Darvince> holy shit [16:35] <syule> darvince it's very close to 1-1/e [16:35] <syule> not exactly though [16:35] <syule> it's a nice form though [16:36] <+Darvince> would it be lower or higher [16:36] <syule> uh [16:36] <syule> higher [16:36] <syule> by a miniscule amount [16:36] <+Darvince> kolok [16:36] <syule> properly it's 1-(292201337/292201338)^292201338 right [16:36] <syule> wait a second [16:37] <syule> yes [16:37] <+Darvince> what is durst [16:37] <+Kalassak> wow [16:38] <syule> the second term simplifies to 1/e [16:38] <syule> as you take the limit [16:38] <syule> so you get 1-1/e [16:38] <syule> bam kalassak change your major to math [16:38] <syule> so you can answer all dar's questions [16:38] <+Kalassak> inpresiiv [16:38] <+Kalassak> that sounds [16:38] <+Kalassak> skari [16:38] <+Kalassak> and boring [16:38] <+Darvince> 1-(2/3)^3 [16:38] <+Kalassak> i prefer applied math thanks [16:39] <+Darvince> I WAS LITERALLY UNABLE TO DO HOMEWORK FOR HOURS BECAUSE I COULDN'T GET MY HEAD OFF OF THAT STUPID PROBLEM [16:39] <+Darvince> WHAT THE FUCK SYULE [16:39] <syule> lol [16:39] <+Darvince> NEVER GO TO CLASS AGAIN [16:40] <syule> yes senpai [16:40] <+Kalassak> kol | |
| Submitted on 2016-01-14 14:48:26 | - 0 + |
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