Example Question #1 : Compound Events
What is the probability that we will roll a one on a six sided die and flip a coin to reveal "heads"?
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:
An intersection is the likelihood that one event will occur with another.
We can calculate that the probability of rolling a one on a six-sided die is:
Now, let's determine the probability of flipping a coin to reveal the "heads" side. A coin has two sides: heads or tails. The probability of rolling heads is as follows:
An intersection is the probability of two events occurring simultaneously; therefore, we need to multiply the probabilities.
Convert to a percentage.