 In this video, we provide the solution to question number 14 for practice exam number four for Math 1030, in which case we have the following situation. A local street vendor asks his customer if she would like to play a game of chance. The vendor has a jar filled with 100 marbles. Of the 100 marbles, 90 are colored black while 10 are colored red. The vendor says that he will reach in and pick a marble at random. If the marble is black, then the street vendor will pay the customer $1. But if the marble is red, then the customer will pay the street vendor $5. The picked marble is replaced after the game, that is you put it back in. If this game were to be played indefinitely, is it more beneficial for the street vendor or the customer? So we have to first calculate what is the expected value of this random experiment. And then based upon the number, we'll see who is it better for. So if X is our random variable, then we want to look for the expected value of this random variable. So the random variable is you're going to draw, the random variable is going to measure what is the money you're going to pay. Do you get, we'll pretend we're the customer here. Do we pay $5 to the vendor or do we pay, or do we get $1 from the vendor itself? So if you reach in there, there's 100 marbles and 90 of them are black. If you get a black one, then the vendor is going to pay us $1. So there's a 90% chance that you're going to get a black marble there, in which case you would then earn $1 in that situation. And then if you draw a red one, there's 10 red marbles out of 100, so there's a 10% chance of drawing a red one. But in that case, you have to pay $5 like so. So when you look at that, it's like, wow, it's much more likely that you're going to win than you're going to lose, but losing is such a high price. Which one is it going to be? Well, let's compute the expected value. That's what we want to figure out here. So you're going to end up with 90 times 1, 90% times 1. So that's going to give you 90 cents there. We'll put a dollar sign. And then for the next one, you're going to get 10% times 5, so that ends up with negative 50 cents there. So in the end, you end up with 40 cents. This is the expected value. So what this tells us is that if you were to play this game over and over and over and over again, then you would expect to on average earn 40 cents each time you play this game. This means that the customer expects to gain 40 cents for each game she plays. Therefore, I would definitely say that the game is more beneficial for the customer. So she's going to win on average when she plays this game. So that is what I would definitely recommend. So when you answer this question, do make sure you calculate the expected value, but you also have to interpret the expected value. Is it better for the vendor or the customer? For this game, how it's structured, it's better for the customer. This vendor is going to go out of business very quickly.