You cannot know what comes next

The idea

A situation is random when its possible outcomes are known but which one will occur cannot be predicted; a random experiment can be repeated, and each time its result may differ and cannot be known in advance.

Heads or tails?

You toss a coin. You know it will land heads or tails. But which one?

Before the toss, can you be sure which side will come up?

• Yes, I can work it out
• No, either could come up

Run the experiment

Guess first, then run each experiment 8 times. Run it again and again. Do you get the same results?

Known results, unknown order

A situation is random when we know every possible result but cannot predict which one will happen.

A random experiment is something you can repeat. Each time the result may be different, and you cannot know it in advance. All we can say is what could happen, not what will happen.

Notes

A random experiment can be repeated. We know all the possible results, but each time the result may differ and cannot be predicted.

Check yourself

Which is a random experiment?

A die is rolled. How many different results are possible?

Answer: 6

The die can show 1, 2, 3, 4, 5 or 6, so there are 6 possible results.

A coin is tossed 10 times. What can we say?

On a random experiment, which can we say before it is done?

• Rolling a die — correct. Yes. We know the six possible results but not which one will come up.
• Adding 2 and 3. The answer is always 5.
• Counting the sides of a triangle. It always has 3 sides.
• The results must alternate: heads, tails, heads, tails…. There is no such rule. The tosses are random.
• Each toss may give a different result, and we cannot know it in advance — correct. Yes. That is what random means.
• All 10 tosses must give the same result. That can happen, but nothing forces it.
• What could happen — correct. Yes. We know all the possible results.
• What will happen. That is the part we cannot know in a random experiment.
• Both what could and what will happen. We can only list what could happen.