Learn about Probability of Compound Events with Number Cubes Compound Events: So, in this problem we need to find the compound events. Rolling two number cubes individually are two simple events but when you find the sum of the outcomes of the two number cubes then the event becomes a compound. A compound event includes two or more simple events. Let’s take a look at our problem. A toy company is developing a game where you find the sum of two numbers you get when you tossing two one through six number cubes. The first problem asks how many possible outcomes are there. For each number cube, there are six possible outcomes when you roll both cubes. If we look at this chart, if we roll both cubes, there are six possible outcomes. I can roll a one, two, three, four, five or six on one cube as I can do on the second cube. If we count the number of squares, we see that there are 36 possible outcomes of rolling two number dice or cubes. Now, there’s also another method of finding the total possible outcomes. The first method was doing this chart. Another method is we can use the counting principle to find all the possible outcomes. The counting principle states that the number of possible outcomes in a compound event is equal to the product of a number of possible outcomes for each simple event. Since we have the possible outcomes of Event A times the possible outcome of Event B, this will give us the possible outcome of the compound event. The possible outcome of Event A is six. We have six possible outcomes. The possible outcome of Event B is six. We have six possible outcomes. Event A is the first cube and Event B is the second cube. If we multiply 6×6, we get 36 which is the possible outcome of our compound event. There are 36 possible outcomes of rolling two number cubes. So, whether we use the model or by the counting principle, we get the same answer. All right, let’s take a look at the first part. How many possible outcomes are there? There are 36. Let’s take a look at Part B. What is the probability of rolling a sum of five? To solve this, let’s look at our table. To use the table to find the number of favorable outcomes and the number of possible outcomes, so from the table, we know that there are 36 possible outcomes of rolling the two number cubes. Out of which four outcomes give the sum of five. If we look, we see the sum of five four times. We know there are 36 possible outcomes of rolling a dice but there are four outcomes of rolling a five. To find the probability of rolling of sum of five, so P(5) is finding the sum of five will equal the number of favorable outcomes over the number of possible outcomes. Therefore, our number of favorable outcomes of rolling a five is four over the number of our possible outcomes is 36 and if we reduce we get 1/9. The probability of rolling a sum of five is one out of nine. Remember that a compound event is an event that consists of two or more simple events. Remember that the probability of event is equal to the number of your favorable your outcomes over the number of the possible outcomes. We can use models and counting principle to find the possible outcomes. Here is the model. Then we can use the counting principle which the counting principle states that the number of possible outcomes in a compound event is equal to the product of the number of possible outcomes for these simple events.