Probability & Statistics

YOU ARE LEARNING:

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?

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

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

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.

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?

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

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.

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?

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.

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

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 $50\%$

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 $0$

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?

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

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

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?

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.

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 $1$ .

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

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.

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?

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

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

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

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.

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.

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.

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.

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.

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 $\frac{5}{20}=\frac{1}{4}$ .