Probability and chance

Ages 13 to 17 Read alone · about 45 minutes

Read together

Probability measures how likely something is, from 0 (impossible) to 1 (certain). Fractions, decimals and percentages can all express it. A fair coin has a probability of 1/2, or 50%, of landing on heads.

Theoretical probability is what should happen, such as 1/6 for rolling a 3 on a fair die. Experimental probability is what actually happened in tests. With more trials, results usually get closer to the theory.

Past results do not change the chances of independent events. After five heads in a row, the next toss is still 1/2. Believing otherwise is called the gambler's fallacy.

Do it

1. Toss a coin 50 times and record the results. How close to half were heads? Combine with others to reach 200 tosses.
2. Roll two dice 50 times and record the sums. Which sum is most common? List all 36 outcomes to find why.
3. Calculate: what is the probability of rolling a 7 with two dice? Of drawing a red card from a deck?
4. Discuss why lotteries and games of chance are designed so the organisers win over time.

Talk about it

• Why is 7 the most common sum of two dice?
• What is the gambler's fallacy?

For the grown-up

Understanding probability helps with decisions about risk, including health and money. It also helps explain why gambling usually loses money over time. If gambling is a concern in your family, talk openly about it with your teen. In the US, the National Problem Gambling Helpline is available at 1-800-522-4700, and findahelpline.com lists help in other countries.

Mark as done

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Where this comes from

• Ian Hacking, The Emergence of Probability (Cambridge University Press, 1975)
• National Council on Problem Gambling (United States), information on the National Problem Gambling Helpline

Written with AI assistance and checked against the sources listed. Please read it before sharing it with a child.