Example Question #1 : Compound Events
What is the probability of rolling "snake eyes"—a value of one on two separate dice—using two fair dice?
In order to solve this standard, we need to understand two primary components: probabilities and the property of independent events. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:
Let's use this information to solve our problem. First, let's calculate the probability of rolling a one. There is a single side of the die that has a value of one and there are six total sides on the die; therefore, we can write the following formula:
Now, let's find the probability of rolling a two on a separate die in the same roll.
Last, we need multiply these two probabilities together.