probability
Probability misconceptions
Fix errors such as thinking a result is 'due' after a run of outcomes.
Quick answer
Probability is about how likely something is to happen, and sometimes people think that if something has happened a lot, it won’t happen again – or that it must happen soon. This is a mistake because each event is separate and independent, like flipping a coin or rolling a dice.Learning outcome
By the end of this page, you will understand that each event in probability is separate and independent, so the chance of something happening doesn’t change just because it has happened a lot or not at all.Why this matters
Understanding probability helps you make better guesses, decide what to do in games, and know how likely things are to happen in real life. It helps you not get confused when flipping coins or rolling dice. It also helps you think more clearly when you hear someone say, “It’s been a while, so it’s bound to happen now!”How it works
Think of a coin flip. Every time you flip it, the chance of getting heads is always 50%. It doesn’t matter if you flip it 10 times and get heads each time. The next flip is still 50% heads and 50% tails. Each flip is its own event. The same is true for dice rolls, card draws, or anything that has a chance of happening.Examples you can see
Let’s imagine you are playing a game where you roll a dice to win a prize. You roll the dice and get a 6. You might think, “Now I can’t get a 6 again!” But no – the chance of rolling a 6 is still 1 in 6 (or about 16.67%) every time. Here’s a table showing the probability of rolling a dice:| Dice Roll | Probability |
|---|---|
| 1 | 1 in 6 |
| 2 | 1 in 6 |
| 3 | 1 in 6 |
| 4 | 1 in 6 |
| 5 | 1 in 6 |
| 6 | 1 in 6 |
Try it as a mini adventure
Imagine you are a detective solving a mystery. You are trying to find a treasure in a box that might have a key inside. Each time you open a box, you have a 1 in 4 chance of finding the key. You’ve opened 3 boxes and found nothing. Now, you think, “The key must be in the next box!” But no – the chance of finding the key is still 1 in 4. Each box is a new chance, not a reward for the past. Let’s play a game! Try rolling a dice 10 times. Record each roll. Now, look at your results. Did you get more of one number than others? Did you think that number was “due” to come up again? That’s a common mistake. Try rolling again and see if the pattern continues.Common mistakes
- Mistake: Thinking that after flipping a coin and getting heads 5 times, tails is more likely to happen next.
- Why it happens: People think that if something happens a lot, it must balance out. This is called the gambler’s fallacy.
- Correct idea: Each flip is independent, so the chance of getting heads or tails is always 50%.
- Mistake: Believing that if you roll a dice and don’t get a 6 for a while, you are “due” to get one.
- Why it happens: This is also the gambler’s fallacy – people think probability must even out.
- Correct idea: The chance of rolling a 6 is always 1 in 6, no matter what happened before.
- Mistake: Thinking that if a coin is flipped 100 times and lands on heads 50 times, it’s “due” to land on tails.
- Why it happens: People think that over a long time, things must balance out.
- Correct idea: Each flip is independent, so even if it's 50-50 over 100 flips, the next flip is still 50% heads and 50% tails.
Parent and carer guide
Parents and carers can help by:- Playing games like dice or coin flips with children and asking them to predict the next result.
- Encouraging children to record results and discuss whether they think the next event is more or less likely.
- Using everyday examples like weather, sports, or games to talk about probability.
- Not worrying if children make mistakes – it’s a common misunderstanding that can be fixed with practice and explanation.
- Reinforcing that each event is separate and independent, even if it seems like it should "even out."
Practice questions
- What is the chance of rolling a 3 on a dice? Answer: 1 in 6
- If you flip a coin and get tails 4 times in a row, what is the chance of getting tails on the next flip? Answer: 50% or 1 in 2
- What is the chance of rolling a 6 on a dice? Answer: 1 in 6
- After flipping a coin 10 times and getting heads each time, what is the chance of getting heads again? Answer: 50% or 1 in 2
- If you roll a dice 5 times and never get a 1, what is the chance of getting a 1 on the next roll? Answer: 1 in 6
FAQ
What is probability?
Probability is how likely something is to happen. It can be shown as a number or a fraction, like 1 in 2 or 50%.
Why do people think that probability "evens out"?
People often think that if something happens a lot, it must balance out. This is a mistake called the gambler’s fallacy.
Can you give an example of probability in real life?
Yes! Like rolling a dice, flipping a coin, or drawing a card from a deck. Each event has a chance of happening, and that chance doesn’t change based on what happened before.
Is it okay to make mistakes in probability?
Yes! Making mistakes is part of learning. Probability can be tricky, but with practice and examples, it gets easier.
How can I help my child understand probability?
You can play games, talk about real-life events, and ask questions about chance. Encourage them to think about whether events are independent or not.