Example Question #8 : Data Analysis, Probability, And Statistics
What is the probability that a person will roll an even number on a six-sided fair die?
In order to solve this problem, we need to discuss probabilities. 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:
The die has six sides with the following values: one tow, three, four, five, and six. Of these values the die has three that are even: two, four, and six. We can write the following probability.
Now, let's convert this into a percentage:
Example Question #1 : Single Events
Two fair dice are tossed. You are not shown the dice but you are told that exactly one die shows an even number. Give the probability that a total of seven was thrown.
Two fair dice can be thrown with 36 equally probable rolls. 18 rolls comprise one even number and one odd number. They are as follows - with the rolls that total seven in boldface:
6 of the 18 possible rolls have total 7, making the probability of a roll of 7, given that exactly one doe shows an even number, equal to .
Example Question #2 : Single Events
Two fair dice are tossed. You are not shown the dice but you are told that at least one die shows an even number. Give the probability that a total of seven was thrown.
Two fair dice can be thrown with 36 equally probable rolls.9 rolls can be thrown that show two odd numbers: they are
This leaves 27 rolls with at least one even number, 6 of which result in a sum of 7:
This makes the probability of rolling a sum of 7
the correct choice.