How to Find Probability of Success on a Single Trial
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In probability theory, when each outcome is equally likely to happen, we say that the experiment has a uniform probability distribution, or simply a uniform distribution.
We write the probability of an event as a fraction. The numerator needs to be equal to the number of outcomes that fit the event . We call this the number of favorable outcomes. The denominator needs to be equal to the number of possible outcomes.
Formula
Uniform Distribution
If all the outcomes of an experiment are equally likely, the probability that the event occurs is:
The probability is always a number between 0 and 1. The sum of the probabilities of all the different outcomes in a sample space is equal to 1.
You will use the formula above very often! It’s really helpful.
Experiment with One Trial
By saying experiment with one trial, we mean that you look at an experiment that only consists of one trial. Rolling a die once is an example of this. Rolling a die twice is an experiment with two trials.
Example 1
You already know that the probability of getting a 5 when you roll a die is . This is because the relative frequency goes towards when you have a large amount of trials.
With the formula above, you can also find the probability of getting a 5 when you roll a die once.
The number of favorable outcomes is the number of outcomes that give you a 5. Since the die has only one side with five dots, the number of favorable outcomes is 1. The die has a total of six sides. That makes the number of possible outcomes equal to 6 when you roll a die. Thus, the probability is
Example 2
You’re at a birthday party, and there are four bowls: The first is filled with Oreos, the second with Doritos, the third with Milk Duds and the fourth with peanuts. Your friend dares you to grab a snack at random, but you would prefer to get Oreos. What is the probability that you get Oreos?
The number of favorable outcomes is 1, since there is only one bowl that contains Oreos. The number of possible outcomes is 4, since there are four bowls in total:
