Describe simple probability using fractions

Probability is represented as a fraction describing the likelihood of an event in a finite set of equally likely outcomes: the numerator counts outcomes favorable to the event, and the denominator counts all possible outcomes. The fraction lies from 0 (impossible) to 1 (certain), can be interpreted and compared on a number line, and may be expressed in equivalent forms; this treatment excludes dependent or conditional probability and nonuniform probability models.

Detailed Explanation: Describe simple probability using fractions

Probability tells how likely an event is to happen.

For equally likely outcomes, use the rule

\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{number of all possible outcomes}}.

Favorable outcomes are the outcomes that make the event happen.
All possible outcomes are every outcome that could happen.

Example

What is the probability of rolling a number greater than $4$ on a fair six-sided die?

Step 1: List all possible outcomes.

A die can show

1,2,3,4,5,6

There are $6$ possible outcomes.

Step 2: Find the favorable outcomes.

The numbers greater than $4$ are

5,6

There are $2$ favorable outcomes.

Step 3: Write the probability as a fraction.

P(\text{number greater than }4)=\frac{2}{6}

Step 4: Simplify if possible.

Both $2$ and $6$ can be divided by $2$ :

\frac{2}{6}=\frac{1}{3}

So, the probability is

\boxed{\frac{1}{3}}.

This means that $1$ out of every $3$ equally likely outcomes is favorable. A probability is always between $0$ and $1$ : $0$ means impossible, and $1$ means certain.

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Probability - Cards, From Hand, Pick One of Group, To Fraction

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