NZ Level 4

Probabilities as Fractions

Lesson

Often we can't be certain of something happening, and we are only able to calculate the chance it might happen. We can think of the chance as having levels, and we may use words such as:

- certain
- extremely likely
- very likely
- possible
- unlikely
- very unlikely, and
- impossible

to describe the probability of something happening.

If we toss a coin, there are $2$2 possible outcomes. We could toss a head, *or *we could toss a tail. The chance of a head is $1$1 out of a total of $2$2 possible outcomes, so we would write this as $\frac{1}{2}$12.The chance of tossing a tail is also $\frac{1}{2}$12. The chance, or probability, of tossing a head *or* a tail is $\frac{1}{1}$11, or $1$1, since it is certain that we will toss either a head or a tail. The chance of tossing *neither *a head nor a tail is $\frac{0}{1}$01or 0, since it is impossible that neither a head nor tail will appear, assuming we are using a standard coin.

If we roll a die, our fractions change, because a die has $6$6 sides. Let's explore this in Video 1.

Sometimes, we might want to work out the probability of more than one thing happening. Instead of working out the probability of rolling a $3$3, for example, we might want to know the probability of rolling an odd number. We use exactly the same method that we use for one particular outcome, but we may find there is more than one way in which we can do this. Finally, we need to express our answer as a fraction in its simplest form, and we do this in Video 2. We also investigate a situation that is certain to happen!

Remember!

If it is impossible for something to happen, then the probability will be $0$0. If something will definitely happen, it has a probability of $1$1.

There are $100$100 cards, numbered $1$1 to $100$100, face down on a table.

What is the probability that Lucy picks a card with a number less than $61$61?

Write your answer as a fraction in its simplest form.

This spinner is spun.

What is the probability that it lands on purple?

Write your answer as a fraction in its simplest form.

What is the probability that it lands on blue?

Write your answer as a fraction in its simplest form.

What is the probability that it lands on yellow?

Write your answer as a fraction in its simplest form.

Xanthe takes a marble out of the jar without looking.

What are all the possible colours Xanthe could choose? Select all the correct answers.

Blue

ARed

BGreen

CYellow

DBlue

ARed

BGreen

CYellow

DWrite a fraction that represents the probability of choosing a red marble.

Write a fraction that represents the probability of choosing a blue marble.

What is the probability of choosing a yellow marble.

Write a simplified fraction that represents the probability of choosing a green marble.

Use simple fractions and percentages to describe probabilities