Using a Simulation to Predict Probabilities

Hey there, it's Mr. Herm with another video. This time we're going to be talking about using simulation to predict probabilities. And in this video we're going to be using simulation that's already done for us. This is one that's already been chosen, so it's going to be just like the homework problem you did previously. It's the one from yesterday. And it's going to be have the It's the one talked about that said would have for you. So, it's the one with the dog. So, let's read it together and talk about it. Here it says, "Use the table of randomly generated numbers below to answer all the questions." And this of course is that table right here. It's the table we're talking about. The Darren created this table of random numbers to simulate three dogs eating food on three different days. So, each of these is dog. Each of these is these numbers. Like for example, if have number 266, this is dog here. This is dog there. And that's dog there. And what are the things that the dogs can do? Well, it says here Darren Darren notices that his his Spotty, his dog, usually drinks when he eats his food, but not always. So, Darren looked it up online research said that 70% of the time, 0.7 is decimal for 70% of the time, when dog eats their food, they take drink of water, too. So, Darren designed simulation to estimate the probability exactly two out of three times that dog eats his food, he also drinks water, too. So, we're going to use the numbers in this case it does say one through seven to represent time when he ate his food and drank water. So, I'm going to write those out as 1 2 3 4 5 6 7. So, those are food and water. The other possibility is the 8 9 and 0s left over. Those are the 30% or the 0.3. So, 8 9 and 0. And on those, it's just food. So, it didn't The animal didn't The dog didn't drink water. They just ate those times. So, we're looking for specific amount here. We're looking for exactly two out of three times that they ate and drank. So, we're looking for two of these and one of these. So, if we look over at the 266 for example, the 266 here has two, which is in the first region, and six, and six, which is also in the first region. Well, that's all three are food and water. We want just two. So, that one's not going to work. I'll just finish going through the first couple rows and then we'll fill them in kind of quickly, and you can pause it and try on your own, too. So, the next one's 342. Well, that's three, four, and two. Those are all again in the first one, so that's no good. That's not exactly two times that the dog ate food and water. Let's try the next one, 847. So, we've got eight, which is in the second one. That's one of those. And look, the four and the seven are both in this group right here. That means that's exactly what we're looking for, one of those. Then we got 672, and can see that have six, seven, and two all in this one. want just two of those. So, that's no good. Let's try 567. Again, five, six, and seven are all here. So, that's no good. What we could do is look for just one eight, nine, or zero. That might be easier. So, on this one notice have one eight. Well, that's going to work. That's good one. Is there one one, eight, nine, or zero here? Definitely not. So, that's not good one. Is there one, eight, nine, or zero here? No. How about here? Is there one, eight, nine, or zero? Yes, there is. There's one nine. That one counts as good one. And the last one again, not one. So, that's no good. So, I'm just going to fill these in kind of quickly, and then we'll go through the questions one at time. And you can pause it if you want and see if you get the same answers. Okay, now that you've turned the pause off and you can see that we actually end up getting the same thing, hopefully, or really close. You might have made couple mistakes. That's okay if you did. Just check and see what those are. So, let's go over the questions right now for number one. One of them says, "What does the number 429 mean?" Well, we actually can look up here and see 429 is right here. So, we know 429 is one we circled. So, if we circle that, that means that two of the dogs had food and water, and one just had food. That's what that means. On the second one, what is the number five 56 mean? Well, could find it in there, but don't see it right off the bat. So, I'll just go with 556. There's here. There's two fives and six, which means all three. So, all three had food and water. And finally, the last question says, "Use the results of the simulation to estimate the probability exactly two out of three." Well, that's what we just did. Up here we found out how many there were. So, we're going to now use the probability to figure that out. It's pretty simple. We're just going to go in and count how many there were. So, let me change the pen here. We're going to count how many there were that had And it's not Let me change it. There we go. How many had food and water twice? So, 1 2 3 4 5 6 7 8 9 10 11 So, we got 16, and it's out of how many there are, which there are 30 of these boxes. It's 5 by 6 box. So, it'd be out of 30, which we can reduce to 8/15. So, the answer to number three is 8/15. Hey, thanks for watching. This is great review video that you can learn from. Don't forget to check out if you get chance to click on my Amazon banners on my website. They send couple pennies my way when you guys buy something on the website. Thanks so much. Have great day.