[MUSIC]. Joe, I've got some bad news, here. >> Alright. >> This, we've got a problem. The machine grader seems like it's broken. >> Broken? [LAUGH]. >> So either you or I are going to have to grade all the mini projects this week. >> Like all 10,000 of them? >> Yeah, yeah. There might be 20,000. [LAUGH] No problem, right. >> Okay. But I figure, like, I don't want to do it so let's, let's flip for it, what do you think? >> Alright, sure, let's go. >> Ready. You call, okay. >> Heads. >> Ooh sorry, it's tails. >> [SOUND]. >> [LAUGH] I don't think it's going to get fixed quickly though. You want to go double or nothing, two weeks? >> Do it. Do it. >> All righty. >> Heads. >> Oh, sorry Joe. >> All right, three weeks. >> Three weeks? >> Three weeks. >> All right on three weeks. Here we go. Here we go. >> Heads. >> [LAUGH] Ooh, no deal. All right you want to to go for four? want to to go for four? >> All right. There's absolutely no wayiIt's coming up tails again. Absolutely. >> What do you think the probability is? >> Let's see. The first one was 50/50. Second 50/50. Third, it's like, like 16 to 1. Or something like that.I mean it's not, there's no way. >> Hey, Lou, you want to educate him? Joe, I wouldn't have expected that mistake from, Scott, not from you. >> [LAUGH] >> [UNKNOWN] has nothing to do with the first three times. So, it is 1/2 that you see a head, 1/2 that you see a tail. >> Its no way Scott wins four coin flips against me. >> [LAUGH] Let's go for it. Let's go for it. Tails. >> Oh, sorry it was heads. [LAUGH] >> Oh, I shouldn't have switched. >> Now the question is what is the probability you had lost four times in a row? I'm going to let Lou answer that one. >> Actually if you give your old answer you have been correct. [LAUGH] >> I see this week is going to be hard for me. >> So this week we're going to actually look at probability. We're going to think about these kinds of questions and we're going to apply it to simple games. Our probability transcends games, obviously, right? Lou, do you want to give us some examples of where we might actually use probability in a more practical setting? >> Sure. Actually, this seemingly useless exercise we just did here is actually, it can illustrate a very important concept, which is the use of DNA profiling in forensics. So, just imagine a scenario where we have a crime, and there's a suspect, and there were witnesses to that. And then the witness comes and says something about the suspect. And let's avoid the usual DNA for now and let's use some tricks. But the suspect says I saw that, that the witness says I saw that the suspect has blue eyes. Now, we bring the suspect and suppose the suspect has blue eyes. Now, we say, okay, it seems that the guy who actually committed the crime. But the question now, what is the probability that we will just get someone with the blue eyes just by chance. So now if we imagine that the population of the world is, has blue, green, brown, and black eyes of equal numbers. Then if you just choose one person at random, the probability that that person will have blue eyes is just one quarter. So now that's not a very reliable test. But suppose now, the witness comes and say, the person had blue eyes and blond hair. And let's assume that these two things have nothing to do with each other. And again, let's assume that the world population has blond hair, black, and brown, one 3rd, one 3rd, one 3rd. So, now what is the probability that the person has blue eyes, and blonde hair? So, now it becomes one 4th, times one 3rd. So, now we stat narrowing down the options that the person has two traits by chance. And, this is basically the idea behind, the use of DNA profiling in forensics. That now you take a, a sample, from, from the crime scene, and you look at the DNA of the suspect, and you look at multiple genes in the sample and in the suspect. And now you ask the question what is the probability that we will see such a match between the two. And the larger the number of genes you have, and the higher the, the match among these genes, the lower the probability that you will see something like that by chance, and this is how this kind of test is used. And this is a very important example of the use of probability in real, world situations. >> So this week, we're going to just look at games like this, but we want you to keep this in mind. This goes way beyond games. There's a lot of interesting applications of probability in computer science.