The link between simple probability and expected frequency is explored using a combination of statistics to investigate risk and its impact on life.

Probability is about estimating how likely (probable) something is to happen.

Probability can be used to predict, for example, the outcome when throwing a die or tossing a coin.

We often use words to describe how probable we think it is that an event will take place.

For example, we might say that it is likely to be sunny tomorrow, or that it is unlikely to snow in August.

Have a look at the statements below, and decide whether the following events are: certain, likely, very likely, evens (neither likely or unlikely), unlikely, very unlikely or impossible.

- You buy a lottery ticket and win the jackpot.
- You toss a coin and get heads.
- Christmas will fall on 25 December this year.
- You grow another nose.
- It will rain in the first week of December.

- Question
A game is played where 7 beads with digits from 1 to 7 on them are placed in a bag.

A bead is taken out, and you then have to guess whether the number on the next one to be taken out will be higher or lower, and so on.

In each case, choose an appropriate word from the following list to complete each sentence:

- certain
- likely
- very likely
- unlikely
- very unlikely
- impossible

Remember that there is only one of each number.

1. If the first bead is 7, what is the chance of the second bead being lower than 7?

2. If the second bead is 1, what is the chance of the third bead being lower than 2?

3. If the third bead is 6, what is the chance of the next bead being higher than 4?

1. The first bead is 7. What is the chance of the next bead being lower than 7?

The numbers remaining are: 6, 5, 4, 3, 2 and 1 so the chance of the 2nd bead being less than 7 is certain.

2. The 2nd bead is 1. The numbers remaining are: 2, 3, 4, 5 and 6. The chance of the next bead being lower than 2 is impossible.

3. The 3rd bead is 6. The numbers remaining are: 2, 3, 4 and 5. The chance of the next bead being higher than 4 is unlikely.