Let’s say that the first five white balls are pulled from the first container containing 70 balls and that the sixth ball is pulled from a second container containing 25 balls. What is the probability then of getting exactly the two lowest numbered white balls from the first container?
I still don't understand your question ... there are several possible interpretations, and I don't know which one you think is the most obvious.
So here's one.
> There are white balls numbered 1 to 70.
> There are black balls numbered 1 to 25.
> I select 5 white balls uniformly at random without replacement.
> I select 1 black ball uniformly at random.
> I place all the balls in numerical order.
> What is the probability that the black ball is the third smallest?
But that description doesn't really seem to match the language you're using. You talk about "Getting exactly the two smallest white balls right" ... I have no idea what you mean by that. And what part is played by the black "mega" ball?
If my framing is right (though I suspect it isn't) ... the first supplementary question is: What if the selected white balls are numbered 1, 2, 3, 4, 5 and the black ball is numbered 2?
By the way, the hardest part about these sorts of questions is learned how to state them absolutely precisely. You will find that no matter how careful you are, there will be someone who finds an alternate interpretation. I'm not even convinced my statement above is completely water-tight.
Also, why are you asking? What's your application?
Finally, as I say, I suspect my framing is wrong, and that I really don't understand what you're asking. If you're serious about this, you need to think carefully about what's actually going on, break it down into very small steps, and try to be absolutely precise about each step. So far, I suspect I'm not going to understand your question well enough to be able to answer.
Let’s say W stands for white ball and B for black ball. Let’s say we draw and order the white balls from least to greatest. It will look like this:
W1 W2 W3 W4 W5 B1
I’m asking what is the probability I get the two lowest white balls W1 and W2 correct but get all other balls W3 W4 W5 B1 incorrect?
What do you mean by "get W1 and W2 correct"? I get the bit about drawing the balls and ordering them. I don't understand what you mean by "get them correct".
That means that if those numbers are drawn randomly from the containers, I’m asking what is the probability that a person guesses those numbers right BEFORE they are drawn as happens in the lottery?
That depends on how the person chose their numbers. So now you need to specify how the person chooses their numbers. Are they choosing their numbers uniformly at random without replacement?
I still don't know that the black "mega" number has to do with this, and I'm still curious as to where the question comes from.
Let’s say the person chooses those numbers randomly and in the same way they are drawn (e.g. no replacement so number 1 can only be chosen once for the white balls).
The black ball is there just to get the exact probability estimate for the Mega Millions lottery.
To answer your question it comes from the Mega Millions lottery which draws 5 white balls and 1 black ball. And I’m curious to know what is probability I get first two numbers right.
Suppose I draw 5 numbers uniformly at random from 1 to 70, and suppose I do so twice. What is the probability that the smallest two numbers match, and no others?
So let a1<a2<a3<a4<a5 be the number from one draw, and let b1<b2<b3<b4<b5 be the number from the other draw. What is the probability that a1=b1, a2=b2, and a3, a4, a5, b3, b4, b5 are all different.
Is that your question?
How accurately do you need to know the answer? You can get an approximation quite quickly by simulation ... an exact answer will be horrible.
Edit: OK, I have answers, but it would be useful to know how accurately you need your answer.
I think doing it on the side is less feasible because (1) work takes up too much time for me to make meaningful progress in say 6 months, it will be very slow progress (2) I find that the best coding bootcamps also help in getting you a software engineering job which I think will be a lot harder just studying on your own
Thanks super helpful. Had a couple of followups: (1) Which boot camp did you attend if you don't mind me asking and in what city? (2) How you find the job interview process? (3) What kind of work are you doing now? (4) Do you feel that today you could learn anything you wanted to learn for example deep learning if you put in time or do you feel webdev is extent of what you can do? (5) What do you enjoy most about it? (6) Enjoy least? (7) What was different than you expected going in? (8) Where do you see yourself going in the future as a software engineer? -- Thanks a ton for your help.
1) app academy San Francisco
2) it was challenging you get rejected a lot, you get tons of homework projects, and you end up having to practice skills that are useless for your job. I am dreading when I have to do the next job hunt (a lot of engineers hate the process). On the plus side most companies will want to interview you because of your background.
3) I am doing full stack web dev. Started mostly on the front end moving more towards the back. I just got moved to a search team.
4) Mostly not. I feel capable of doing web dev, mobile, and possibly embedded stuff. I do see myself able to get into machine learning within 4 years but that's because of my stem and math background. It is true though that by being a web dev many large companies will let you work on a team with machine learning guys so you can hustle your way in. Just don't think a bootcamp will give you the knowledge.
5) I like building things. I don't care that most of the things I build are crud apps, I have so much pride in being able to see something I built in the real world.
6) I feel lost and dumb a lot of the times. I realize now this feeling will never go away as an engineer - it's a part of the job.
7) I don't enjoy programming as much over the weekends. Before being an engineer I used to work on small coding projects on the weekend and loved it. Now that's it's my job I look forward to doing other stuff. It's kinda like how some NBA players probably don't want to play basketball in the offseason even if they love basketball.
8) I plan to move past web dev and go into something like computer vision or embedded systems. This will take several years but I think I can do it because I have a strong math background.
FYI I agree with many of the commenters that your reasons for doing a bootcamp seem a bit misguided. I did one because I'm genuinely excited by building things. I feel like I could be building boring crud apps for the next 5 years and I'd still be happy. If you don't feel that I would reconsider.
Thanks for the responses guys. A few more points of clarification. PM means product manager. Top 3 tech think Google, Facebook, Amazon, Apple. In terms of my motivation I think today we are where the internet was in 1994-95, at the cusp of the next big technology wave. I think technologies like deep learning and AI more broadly will fundamentally change every single industry and the next big tech companies will be created during this period. Not knowing how to code I think places me at a big disadvantage when it comes to the software jobs that will open up and at a disadvantage if I want to take a stab at starting a company using these technologies. It is a risky bet for sure, but if I think long-term I have a feeling learning to code and being immersed in engineering by working as a software engineer will be a very smart move. But I could be completely wrong lol :)
You seem to care very much about the social appearance : "i work at a top 3 blabla", " i have a MBA from a top 3 school blabla".
Working as a web developer won't get you extra karma points. If you care so much about social appearance and are the kind who enjoy comparing salary income at mundane dinners out, stick to the job you don't enjoy.
If you like programming, you like building things, you like scratching your mind over complex problems, etc... then follow your heart and train yourself for your next career move. Sticking to some kind of social implicit rules isn't necessarily the way to go. Time may prove you right!
I know heaps of people who totally switched career for various reasons : went from a director position to a manager position, went from a PM position to working as a farmer, transitioned to web dev etc... and didn't regret their decision.
No, you're not crazy. Source: I quit a six-figure job as a PM to do a bootcamp and am now working as a software developer at ThoughtWorks.
If you're viewing the decision purely in terms of $$$ (as many other commenters here seem to be doing), it's true that in 10 years you will have earned less money on this path than you would have earned while remaining a PM.
But will you be happier day-to-day? I certainly am. Both careers are well-paid, so why would you pass up a net gain in happiness to earn 15% - 20% more over 10 years? Your happiness is unlikely to change materially because of the extra money, but it could change materially if you start to love your job.
I think a lot of the people giving advice here are software developers who've forgotten what it's like to be unable to build something, with their own hands, that they want to exist in the world. That's such a powerful feeling, especially if you want to start a startup one day.
I did a bootcamp at the beginning of 2013. At that time there were no bootcamps in Australia, so I moved to Chicago for 3 months to do the Starter League (now part of Fullstack Academy). Being in a different city meant I could focus all my energy on the bootcamp. I think this is main advantage of a bootcamp: forced focus for a long period of time, so you learn much faster than you would if distracted by your full-time job.
When I finished the bootcamp, I probably could have been hired as a Junior sometime after an extra month or so of filling gaps on my own, leaning things like TDD and various computer science concepts (algorithms, data structures etc.) My journey personally took longer because I got distracted by travel and other stuff.
As some of the other commenters pointed out, you're probably not going to be able to work on blockchain and machine learning on day #1. You won't have those skills coming out of a bootcamp. You'll probably need to get a job doing Rails or something - don't expect the big 4 or anything like that - and learn that stuff on the side. I would expect you will spend 1 - 2 years doing general software development before you can start working on cutting-edge tech.
But keep in mind that the organisations that do cutting-edge tech are going to be strongly biased toward people with a CompSci degree. Unless you're willing to do a degree, you'll need to learn this stuff really thoroughly on your own and then build some kind of project to demonstrate that you know it. For example, a cool machine learning project. Your bootcamp alone isn't going to get you into these kinds of companies.
You're not going to be able to do a bootcamp and then stop learning. The learning is never going to stop for you. But I think what you're planning to do is doable in a few years. In a few years I went from writing requirements as a PM to writing software to help scientists count mosquito eggs in a lab using image processing. Guess which one was more rewarding?
I suspect the salary difference will be a LOT more than 15 to 20%. More like 50% at first, and tough to close that gap (he might get on a fast track, but he'd also have gotten raises as a PM).
According to Glassdoor, Product Manager at Google is something like 200K/year (an MBA should be making more), Facebook is similar, and Apple a little less.
A bootcamp graduate shouldn't be making more than 100K/year from what I know of the U.S. (might be wrong).
Maybe his credentials make him hired at a higher salary, but nowhere near his former one.
