### All TACHS Math Resources

## Example Questions

### Example Question #1 : Probability Of Compound Events

When rolling a fair six-sided die and flipping a fair coin, what is the probability of rolling either a or a and getting heads on the coin flip?

**Possible Answers:**

**Correct answer:**

Recall what a probability is:

Start by finding the probability of rolling either or on a die. Since there are a total of different outcomes, and we only want these two, the probability must be .

Next, find the probability of getting heads on a coin flip. Since we only want heads and there are only possible outcomes on a coin flip, the probability of getting heads is .

Since the question wants the probability of both events occurring, you must multiply the probabilities together.

### Example Question #1 : Probability Of Simple Events

What is the probability of rolling a one on a fair die?

**Possible Answers:**

Cannot be determined

**Correct answer:**

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:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

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