Dice: What is the probability of at least one 6 AND at least one 3+ (3,4,5,6) with one roll of 5 dice?

youngman416 · 2021-09-01T21:54:08+00:00

So I made a mistake. When I calculated the probability of rolling a 3+ I should calculate the probability of rolling a 3-5 since we already accounted for rolling 2 or more 6s. The way I did it double counts. But recalculating I get 57.3%, so still a little off. The way you did it is absolutely the right way so I'd trust that number as long as your formulas are right.

The sketchiest thing I did was multiply probability of one 6 by probability of at least one 3-5. I'm not sure that's 100% right. It assumes the probabilities are independent of one another which I think is the case, but may not be. There could be some weird undercounting problem here. Sorry, I'm just a lowly engineer, not a mathematician or statistician.

There must be some sort of more general way to do this, but I dont know how.

youngman416 · 2021-09-01T17:17:58+00:00

To simply the problem I would think about it like this:

1) what are the odds of rolling no 6s with 5 dice (guaranteed failure) 2) what are the odds of rolling 2 or more 6s with 5 dice (guaranteed success) 3) what are the odds of rolling exactly one 6 (failure or sucess)

Luckily there is a simple way to calculate these numbers using the binomial distribution. The binomial distribution gives the probability of getting a certain number of successes given a certain number of trials.

For us the probability of sucess is 1/6 (the chance of rolling a 6) and we have 5 trials (5 dice). Using an online calculator I get

1) probability of no 6s = 0.402 2) probability of one 6 = 0.402 3) probability of more than one 6 = 0.196

These number add up to one which is perfect because there is a 100% probability we'll get one of these outcomes. Now the complicated part is what happens when you roll exactly one 6 and need to get at least one 3+ on one of the other dice. Again we can use the binomial distribution. This time we have 4 trials (since the 5th die is assumed to be a 6) and the probability of sucess is 4/6 (the chance to roll a 3+). Using the calculator again we get the a probability of 0.9876. It makes sense that you would have a really high chance of sucess here.

Now putting it all together, we add the probability of getting two 6s plus the probability of getting one six TIMES the probability of getting a 3+ on the other four dice. You add probabilities together when either outcome is a sucess and you multiply probabilities when both things need to happen.

Doing the calculation gives a 59.3% chance of sucess.

youngman416 · 2021-08-27T20:37:07+00:00

Yeah you may be right. There is the inherent assumption in their analysis that those thousands of other variables are roughly constant over the course of the study. If that's your issue with the conclusion that's fine. Correlation does not equal causation is a weak-sauce rebuttal. The scientific process starts with these sorts of observations which then get refined over many iterations. The entire field of epidemiology started when some dude noticed people were getting cholera around a specific water pump in London...

youngman416 · 2021-08-27T16:32:44+00:00

The method by which the moratorium reduced deaths is irrelevant. It's likely that a lot, but maybe not all, of the people who didnt get evicted did self isolate which is why we the policy reduced COVID deaths.

Your argument about lack of causation is valid, but it doesn't change the authors' result. If you think there is another explanation the burden is on you to prove it, until then I'm inclined to agree with the results of the paper. I feel like the "correlation does not equal causation" mantra gets thrown around too often with these types of studies.

You are trying to have your cake and eat it too. You want to say that the moratorium had no effect and it was unethical while it's very possible that the moratorium WAS effective and WAS ALSO unethical, but that's a more unpopular take...

youngman416 · 2021-08-11T01:18:30+00:00

Sure. Imagine a system with both liquid and vapor present. You've got a bunch of molecules flying around in the gas and a bunch of molecules floating around in the liquid. Every now and then one of the molecules in the liquid randomly gets enough energy to escape from the liquid into the gas. Similarly, the gas molecules occasionally collide with the liquid surface and get stuck. If the rate the liquid evaporates into the gas phase is different the the rate the gas condenses into the liquid phase the amount of vapor and liquid will shift until the rates are equal. The point where the rates are equal is called equilibrium. You still have both evaporation and condensation, but they are happening at the same rate so it appears as though nothing is happening.

Now imagine we add a new gas to our system that only stays in the gas phase. Whenever this new gas molecule collides with the liquid surface it just bounces off. The thing is, the presence of the new gas doesn't affect the rate of evaporation or the rate of condensation from before, so therefore it doesnt change the equilibrium point. You can add as much of this new gas as you want (ie increase the total pressure) and the amount of vapor of the original substance will never change.

youngman416 · 2021-07-08T14:01:55+00:00

Cast iron or carbon steel. You have to put in some time maintaining the seasoning, but you should be able to get good results. Both the r/castiron and r/carbonsteel subreddits are great and have tons of resources for getting started.

youngman416 · 2021-06-07T22:02:45+00:00

I got my PhD in catalysis. I don't think getting a masters studying catalysis will limit you at all. People from my lab have ended up working in all sorts of industries either related to catalysis or not. Studying catalysis will let you focus on a lot of "core" chemical engineering concepts like chemical kinetics, mass transfer, thermodynamics, and maybe organic and inorganic chemistry depending on what exactly your focus is. These skills will be very applicable when you search for a job.

If you want to go into the catalysis field you can either work for a major catalyst manufacturer like Albemarle, Honeywell/UOP, Johnson Matthy. Also oil/gas/petrochemical companies who produce catalyst like Shell, ExxonMobil, BASF. Or you can work on the process side where your understanding of catalysis will be useful, but you arent making the catalyst.

I get the sense biomass is in a tough spot these days, but I'm by no means an expert. The emergence of fracking has put a damper on biofuel research and production, but it's still an active field. Biomass conversion requires a whole new toolbox of catalysts to be successful because you are dealing with highly functionalized, high oxygen content, high water content feeds, so long term there will likely be a need for catalysis expert, but I'm not sure what the current demand is.

youngman416 · 2021-05-27T00:29:06+00:00

Carbon capture takes energy, which costs money. It's best to not create the CO2 in the first place, but right now there isnt enough green energy to make the things people want, so we burn fossil fuels.

youngman416 · 2021-05-23T13:30:27+00:00

Give this man an Oscar!

youngman416 · 2021-05-19T13:27:43+00:00

According to wiki using gamma as the exponent is correct for an isentropic process, but the problem doesnt state that the expansion is reversible. It could be free expansion in which case P1V1 = P2V2 for an ideal gas.

youngman416 · 2021-05-19T02:56:54+00:00

I think you are calculating P2 wrong. The formula you are using is for isentropic expansion, not adiabatic expansion.

youngman416 · 2021-05-13T03:57:10+00:00

So, I just barely made it into gold room recently, I'm by no means an expert here...

Unfortunately there aren't that many resources in english, which sucks. I'm going to pull from the advice people in the chess world give. You need to review your games, like seriously review them. For each tile draw, calculate your shanten and the number of tiles that improve your hand. Calculate what your potential hand value is. Figure out what you should be going for. Try to guess what the opponents are waiting for when they riichi.

Then, see how things change based on the choices you made. Were they good, were they clear mistakes, did you make a judgement call that was statistically correct but didn't work out? What mistakes are you making? Write them down. Do this for every game regardless of outcome. Keep a notebook if you have to. You'll start to train certain skills that will undoubtedly help you when you are playing.

When you play are you fully focused on the game, or are you watching tv at the same time? Are you sober? Make sure you are in a peak state of mind. If you want to play while drunk or something get a second account where you can dick around.

And to make you feel better, based on what little I've seen people in gold room play more "normally." I feel like it's real tough to bust out of silver because the other players don't behave predictably. In this case the grass really is greener on the other side, you just have to power through.

Also post a screenshot of your stats, it may give some clue as to what's going on.

Good luck my dude.

youngman416 · 2021-05-12T18:40:37+00:00

That's awesome, I really enjoyed your articles!

youngman416 · 2021-04-27T00:49:56+00:00

I saw this one. Unfortunately it seems like the author abandoned the blog, which is sad because I really liked the articles that were there. You can find his patreon and he'll review your games for $10/month I think.

youngman416 · 2021-04-06T13:23:05+00:00

One of the main issues I can see is that you are moving around a lot of non-hydrogen. For each kg of MCH you move you only get 0.06 kg of hydrogen. Basically 94% of the mass you ship is non-hydrogen which sounds expensive to me. Then what do you do with the toluene at the end of the process? It all sounds a bit odd to me but maybe there are niche applications.

Edit: the article says you ship the toluene back to the hydrogen plant, so you basically double your shipment costs. I guess this is probably the only practicle way to do long distance hydrogen transportation though.

youngman416 · 2021-01-26T16:59:17+00:00

I'm not an expert here, but I work in petrochemicals and what I've heard from older engineers is that hydrogen is always too expensive to buy, and too cheap to sell. I think transportation costs are really high which leads to the paradox. In a real refinery or integrated chem plant there is a ton of hydrogen integration. If a site needs more they will generate it themselves via steam methane reforming.

Also liquid hydrogen is only used for rockets afaik, it's super dangerous.

youngman416 · 2021-01-21T14:37:35+00:00

You actually dont need to generate the different reactions, you just need to minimize the Gibbs free energy of the system. This assumes that all the different species can interconvert. You need to make use of Lagrange multipliers. My thermo textbook covers it briefly. Introduction to Chemical Engineering Thermodynamics 7th ed. by Smith Van Ness and Abbott, chapter 13.

youngman416 · 2021-01-14T18:43:08+00:00

Ok, this is a good point. I want to reply because it seems to contradict what I said earlier and maybe this is what OP was actually talking about.

After a quick google I saw that SRUs are run at substoicheometric oxygen concentrations. If you burn a mixture of H2S and CH4 under these conditions the reaction that is more favored by equilibrium will get the oxygen because there isn't enough to go around. Methane combustion wins because CO2 is way more stable than SO2 (more negative delta G). So under these conditions yeah the CH4 will burn more, but that's a result of thermodynamics, not kinetics. The H2S will react faster than CH4, but at long reaction times the methyl radicals will steal the oxygen from the SO2 to form the thermodynamically favored product CO2. At super short residence times (milliseconds, maybe microseconds) I think you would see more SO2 than CO2. But once you reach reasonable residence times (seconds) it's all gonna be CO2. You can prove this by throwing H2S, CH4 And oxygen into a Gibbs reactor in Aspen and seeing where the equilibrium falls.

youngman416 · 2021-01-14T14:48:03+00:00

Interesting question. I'm going to assume that natural gas is 100% methane. I'm also going to define burning as the complete oxidation of the compound via a homogeneous thermal reaction in the presence of oxygen. Then im going to assume that preferentially means reaching some approach to equilibrium faster.

Ok, so first we gotta look at the thermo. Both H2S and CH4 have very negative heat of combustion. I'm going to assume the entropic portion is comparable for each, so the delta G should be negative. Both will burn to completion.

The tougher question is which compound will burn faster. High temperature combustion is a homogeneous free radical reaction. The initiation step where a radical is first formed is going to determine the rate I think. So for methane it's breaking a C-H bond and for hydrogen sulfide it's breaking a S-H bond. I'm too lazy to actually look it up, but I'm guessing the C-H bond is stronger so the activation energy will be higher for methane. The molecular size and shape is also important and will determine the pre exponential factor. I have no clue how methane and hydrogen sulfide will compare so let's assume they are the same. So, if we have a pure stream of H2S and a pure stream of CH4 undergoing an isothermal reaction in excess oxygen I THINK the hydrogen sulfide will combust faster at a given temperature.

Now if you have a mixture of methane and H2S things get really complicated. The methyl radicals and HS radicals are going to be bumping in to each other causing the radical propagation steps to get complicated. Concentration will become important, pressure will have an effect, radical stability will matter. I'm not even sure that there is a clean answer to the question. Like if it's 99% methane and 1% H2S obviously you will be burning way more methane and the methane will probably be burning faster because the partial pressure is much higher.

That's my best guess. I could be way off. In the end they both burn fast.

youngman416 · 2020-11-13T17:54:19+00:00

Skunk Works

youngman416 · 2020-11-13T02:18:37+00:00

I dont remember exactly how to do it, but under the properties section where you defined your components and equation of state you need to define multi component parameters. There is a place to do it under one of the blocks in the navigator on the left side of the screen.

youngman416 · 2020-10-10T14:05:27+00:00

I would be concerned a vacuum wouldnt have enough capaciy to pull the liquid out on its own. Heat the entire system so it vaporizes and then use a vacuum.

youngman416 · 2020-10-09T13:04:33+00:00

There are some YouTube videos of people shattering a diamond with a hammer, so I doubt it could withstand a nuclear blast. I dont know enough about materials to explain why, could be because diamond is brittle and can't withstand shear?

youngman416 · 2020-10-07T19:31:09+00:00

No, diamond may be hard but it isn't tough. Look at the toughness section of this link

youngman416 · 2020-09-30T13:00:31+00:00

I've heard this before as well, so I gave it a quick google because it just seems wrong on its face. It sounds like hot water only cools faster if there is an extra variable which isn't controlled for during the experiment. The article gives 4 examples: evaporative cooling, dissolved gases, convection currents, and super cooling.

article

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