Multiplication Rule (GID)

SWARTWOOD PREP
A free video tutorial from SWARTWOOD PREP
Testprep Company in Los Angeles, CA
4.7 instructor rating • 4 courses • 892 students

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Introductory Probability (A Crash Course)

From Permutations & Combinations to the Law of Total Probability

01:34:23 of on-demand video • Updated January 2019

  • You will be able to handle any sort of PROBABILITY problem you are likely to see on a standardized exam, save for the Math Subject GRE [for those going to math graduate school] (assuming you put in the time)!
  • You will have a good working knowledge of foundational probability without too much formalism.
English [Auto] So are you guys real sport with MBA students. Okay. Okay. It's all good. It's all good. So what I'm gonna do is I'm going to reteach this from scratch and I'm gonna build them problems. How are the homework problems. I guess there's standard from that book right. Okay so let's do some self accounting so we just start from scratch. It really will be that simple. Then we will we'll go this pretty quickly if I have two hats two pairs of shirts. I mean two shirts three and like four pairs of pants. How many different outfits can I make. You just do three times two times. I know that's cheesy but it's good for you to believe this intuitively when you have different choices and you're putting them together. We multiply and only for this once I'll just start to do this silly thing. So say like we had three hats like this hat the Santa hat and I don't know the Mickey hat whatever. Something like this. So if you had three hats you choose one of them. Then how many shirts do you get to choose. Two of them maybe the red shirt or the blue shirt the red shirt or the blue shirt the Red Shirt Blue Shirt just to show you this one time and then you can see after that you would choose the pair of pants. It's not hard to believe that three choices for this for each one of these you have two of them. You can see it's three times two. It really does multiply. Right. And if every one of these is for more so it would be then answer times for that believable it's interesting to do this. The reason why 3C is so tricky is you need to build some intuition for it not just the stupid formulas but are we okay with this. Okay. So that's the No. Then I want to push this up to our next thing. In fact let's do a problem with this right now. So you that even at this level. It could be like stressful. So I got 50 people or maybe 40 people and I want to give them each three treatments. I want you to give them drugs alcohol or nothing. So anybody who's psycho bio if you go second take a hundred a year to definitely do something like this was kind of day. Okay. So drugs alcohol nothing. Not not only combinatorial fashion but this idea. So three treatment plants I want to give every single person a treatment. How many different ways can I do this. So I have 40 different people I want to give them each a treatment. Obviously you can use more treat one treatment more than once. Otherwise you can treat everybody right. I want to know how many different ways can you do that. So very like drugs alcohol alcohol that's different from alcohol drugs drugs. When you talked about combinations and permutations so forget that junk. Can you tell me how many ways can you do that and don't let the way I drew the picture for you because the only thing we know how to do is if you make a choice you do what you multiply right. So can you tell me a way to maybe think of this went twenty one point is not that but you're using a permutation I talked about that everything will be fair but to say that what's going on. Because I'm trying to give. Everybody gets a treatment and I do it for all 40 people given three to the. I like that. I like that. So let's think about what happens. So there are 40 people out there right. Just give them names. Here's Person 1 after person 40. These are not numbers these are just names. Right. So here are these 40 people. How many choices do I have for the treatment I give Person 1. 3 I kick them drugs alcohol or nothing. So I have three choices. You guys agree. Once I do that I can reduce it. So for person number two how many choices do I have. Three. And don't you guys agree. I have three choices for every single person here. OK. But remember the golden rule when you're in the middle of making choices before you get your final outcome. I'd like to wait. Multiply. I know it sounds stupid now when we start doing harder problems it'll make sense. So we just multiply three choices for the first person based on that three for the next three for the next. So the actual answer is wait three to the 40. There are three to the 40 ways of doing this because this is not we're like we're using my formulas but the thing is like do I do it this way or do I do it that way. So framing really helps but are we okay with this. OK OK OK. So listen this guy with no stress I'm assuming the regular palms he be comfortable with. That's why I give you one of the slightly more annoying. Ok so this guy's gone. OK so now let's get to it. Everybody.