The sample space refers to possible event outcomes. Subsets of this sample space can be used to compute simple probabilities. See the following examples on how to use this approach.
Example 1
Let's start with a simple example to warm us up:
We're flipping a fair coin and we want to find the probability of getting "heads". We can begin our thought process by first determining all of the possible outcomes. In this case, we can 1) flip and get "heads" or 2) flip and get "tails". Therefore there are 2 possible outcomes = heads, tails
Next, we want to identify which of these outcomes are our desired outcomes, meaning the outcome(s) we are trying to find the probability for. Since we want to find the probability of getting "heads" desired outcome = flipping heads. Looking at our possible outcomes, we can see that only one outcome would be included in our desired outcome: heads.
Now we have everything that we need to compute the probability:
Number of successful/desired outcomes = 1
Total number of possible outcomes = 2
Therefore, the probability of flipping a fair coin and getting "heads" is 1/2. We could also report this as a decimal (.5) or a percentage (50%).
Example 2
Let's look at another simple example that has a few more possible outcomes:
This time, let's roll a fair die. We want to find the probability of rolling a 3. We will again begin by first determining all of the possible outcomes. In this case, we can roll a one, a two, a three, a four, a five, or a six. Therefore there are 6 possible outcomes = 1, 2, 3, 4, 5, 6
Next, we want to identify which of these outcomes are our desired outcomes, meaning the outcome(s) we are trying to find the probability for. Since we want to find the probability of rolling a 3, the desired outcome = 3. Looking at our possible outcomes, we can see that only one outcome would be included in our desired outcome: 3.
Now we have everything that we need to compute the probability:
Number of successful/desired outcomes = 1
Total number of possible outcomes = 6
Therefore, the probability of rolling a 3 is 1/6. We could also report this as a decimal (.167) or a percentage (16.7%).
Example 3
Let's consider another die example:
This time, we want to know the probability of rolling an odd number. Applying the same thought process to this scenario, the possible outcomes remain the same: 1, 2, 3, 4, 5, 6. The desired outcomes now include 1, 3, and 5. That means that there are now three desired outcomes. This means that the probability of rolling an odd number is 3/6 = .5 = 50%
