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How to Find Probability of Success on a Single Trial

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 A as a fraction. The numerator needs to be equal to the number of outcomes that fit event A. We call this the number of favorable outcomes. The denominator needs to be equal to the number of possible outcomes.


Uniform Distribution

If all the outcomes of an experiment are equally likely, the probability that the event A occurs P(A) is: number of favorable outcomes number of possible outcomes

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.

Probability with One Trial

By saying probability 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 1 6. This is because the relative frequency goes towards 1 6 when you have a huge amount of trials.

With the formula above, you can also find the probability of getting a 5 when you roll a die.

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. Then the probability is

P(5) = 1 6.

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:

P(Oreos) = 1 4.

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What Does Uniform Probability Mean?