Albert Teen YOU ARE LEARNING:  What Is Probability?  # What Is Probability? ### What Is Probability?

You can express the probability of unknown events on a scale from certain to impossible. You can also express them as fractions or in percent.

What does probability measure? 1

With a normal 6-sided die, what is the probability of rolling a number less than $7$?  2

Rolling a number smaller than $7$ with a normal 6-sided die is certain. How can we express this as a percentage?  3

An outcome that will always happen is a "certain" probability

A certain probability is the same as a probability of $100\%$

It is certain that you will roll one of $1$, $2$, $3$, $4$, $5$ or $6$ when you roll a normal 6-sided die. It will happen $100\%$ of the time. 1

We have seen that it is a certain probability that we will roll a number less than $7$ on the die. What is the probability that we will roll a $7$ or higher?  2

A certain probability happens $100\%$ of the time. An impossible probability never happens, what percentage is this?  3

An outcome that will never happen is an "impossible" probability

For example, it is impossible that you will roll a $9$ on a 6-sided die. It will happen $0\%$ of the time. 4

This shows us the probability scale from impossible to certain.

In percentage, the scale goes from $0\%$ to $100\%$. Certain probability is $100\%$ and impossible probability is $0\%$. Between those two is $50\%$, what term describes a $50\%$ probability? 1

There are eight balls in this bag, four are red and four green. Is this statement true or false? If you close your eyes and pull a random ball from this bag, it is more ** likely that the ball is red than that it is green.  2

What is the probability of pulling a green ball from the bag?  3

So if the probability of something happening or not happening is the same, it's an "even chance"

For example, there is an even chance between randomly pulling a red ball out of this bag and it not being a red ball. In both cases, the probability is $50\%$ 1

You can put probability on a scale like this

Certain probability is $100\%$ or $1$

Even chance is $50\%$ or $\frac{1}{2}$

Impossible probability is $0\%$ or $0$ 2

This shows the scale for probability from impossible to certain with even chance in the middle. What word describes the section between Even chance and Certain?  3

We can see that a probability between even chance and impossible is unlikely.

However, even if the probability is unlikely it can still happen. 1

This bag contains seven balls, six are red and one is green. Which phrase describes the probability of pulling out a ball which is green?  2

The probability of pulling out the green ball is unlikely.

We can also say that is it less likely to pull out the green ball than a red ball. 1

We saw on the probability scale that an even chance can be shown as a percentage $(50\%)$ or a fraction $(\frac{1}{2})$.

Probabilities can expressed in different ways, but the scale always sits between $0$ and $1$. 2

The bag contains a total of $10$ balls. What is the probability of pulling out a green ball as a fraction?

$3$ are green $3$ are purple $2$ are yellow $2$ are red  3

To find a probability as a fraction.

Work out the number of possible outcomes (in this case three green balls) out of the total number of options (in this case the ten balls) and write as a fraction. 1

There are $20$ balls in this bag, $15$ are yellow and $5$ are purple. Which term describes the probability of pulling out a yellow ball?  2

With $15$ yellow balls and $5$ purple, what is the probability of pulling out a yellow ball as a fraction?  1

Summary! Probability is a measure of how likely something is to happen

You can express it in words, as fractions and in percent. 2

Impossible probability is when something will never happen, so $0\%$ of the time.

It's impossible to roll a $7$ with a normal 6-sided die. 3

Unlikely probability is when something is less likely to happen or between $0\%$ and $50\%$.

It's unlikely that you will pull a green ball out of a bag if only $\frac{3}{10}$ balls in the bag are green. 4

Likely probability is when something is more likely to happen, or between $50\%$ and $100\%$.

It's likely that you will pull a purple ball out of a bag if $\frac{7}{10}$ balls in the bag are purple. 5

Certain probability is when something will always happen or $100\%$ of the time.

It's certain to roll a number smaller than $7$ with a normal 6-sided die. 6

Even chance is when something is just as likely to happen as it is to not happen or $50\%$ of the time.

The probability of rolling an even number with a normal 6-sided die is even chance because that will happen $\frac{3}{6}$ or $\frac{1}{2}$ the time. 7

To express a probability as a fraction take the number of possible outcomes out of the total number of options.

Here the probability of pulling out a purple ball is $\frac{5}{20}=\frac{1}{4}$. 