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Probability & Statistics: fun facts and quiz
The essentials in 7 ideas, with fun facts, an illustrated story and a quiz to see how much you know.
The essentials
What Probability Means
Probability measures how likely something is, from 0 (impossible) to 1 (certain). A fair coin has a 1 in 2 chance of heads: 0.5, or 50%.
Key fact
A fair die gives each number a 1 in 6 chance.
The Gambler’s Fallacy
Coins and dice have no memory. After five heads in a row, the next flip is still 50/50. Feeling that tails is “due” is the gambler’s fallacy.
Key fact
Each flip of a fair coin is independent of the last.
Mean, Median & Mode
The mean adds up the values and divides by how many there are. The median is the middle value. The mode is the most common one.
Key fact
A single billionaire moves the average income a lot, the median barely.
Reading Chances
Chances can be written as fractions, decimals or percentages: 1/4, 0.25 and 25% are the same. A 30% chance of rain means rain on about 3 in 10 days like this.
Key fact
1 in 4, 0.25 and 25% all mean the same chance.
The Birthday Paradox
In a group of just 23 people, there’s about a 50% chance that two share a birthday. It feels wrong, but 23 people make 253 possible pairs.
Key fact
With 70 people, a shared birthday is over 99% likely.
Correlation vs Causation
When two things rise together, they’re correlated, but one may not cause the other. Ice cream sales and sunburns both rise in summer because of the sun.
Key fact
A correlation alone never proves that one thing causes another.
Samples & Surveys
Surveys ask a sample instead of everyone. A well-chosen random sample of about 1,000 people can reflect a whole country within a few percent.
Key fact
Bigger samples help, but a biased sample stays biased.
Fun facts
Coins aren’t perfectly fair: in a study of over 350,000 flips, coins landed on the side they started about 51% of the time.
In 1913, a Monte Carlo roulette wheel landed on black 26 times in a row. Gamblers lost millions betting on red.
Most people have more legs than average: a few people have fewer than two, and nobody has more, so the mean sits just below 2.
Over a lifetime, you’re far more likely to be struck by lightning than to win a big national lottery jackpot.
In many countries the most common birthdays fall in September, about nine months after the winter holidays.
One famous chart shows US cheese eating tracking deaths from getting tangled in bedsheets. Pure coincidence.
In 1936, a US magazine polled over 2 million people and still predicted the wrong winner of the presidential election.
Story: A Gambler’s Question
A Gambler’s Question
Paris, 1654. The Chevalier de Méré, a keen gambler, can’t work out why one of his dice bets keeps losing him money.
He asks the brilliant Blaise Pascal, who starts writing letters about it to another mathematician, Pierre de Fermat.
In those letters, the two worked out how to count chances fairly. Probability theory was born from a gambling puzzle.
True or false?
Tap your answer to see if you got it, and why.
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Question 1 of 10
A probability of 1 means something is certain.
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True. 1 is certain, 0 is impossible, and everything else sits in between.
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Question 2 of 10
After many heads in a row, tails becomes more likely.
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False. Each flip is still 50/50. The coin doesn’t remember.
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Question 3 of 10
The median is the middle value when data is in order.
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True. Half the values sit below it and half above.
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Question 4 of 10
A 25% chance is the same as 1 in 4.
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True. 25 out of 100 is the same as 1 out of 4.
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Question 5 of 10
You need about 183 people for a 50% chance of a shared birthday.
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False. Just 23 people are enough for about 50%.
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Question 6 of 10
If two things are correlated, one must cause the other.
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False. They may share a hidden cause, or it may be chance.
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Question 7 of 10
A survey has to ask everyone to be useful.
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False. A random sample of about 1,000 people can be accurate to within a few percent.
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Question 8 of 10
A probability can be greater than 1.
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False. Probabilities run from 0 to 1, or 0% to 100%.
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Question 9 of 10
Each roll of a fair die is independent of the one before.
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True. The last roll has no effect on the next.
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Question 10 of 10
The mean and the median are always the same.
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False. They match for evenly spread data, but one extreme value pulls the mean away.
Keep going in the app
KnowSoda learns what you know and brings back what you’re about to forget. Probability & Statistics has 6 more ideas at the Advanced and Expert levels.
Sources
- Khan Academy — Statistics and probability
- Bartoš et al. (2023), “Fair coins tend to land on the same side they started”
- UK Met Office — What does a percentage chance of rain mean?
- Encyclopaedia Britannica — birthday problem, gambler’s fallacy, sampling
- Pew Research Center — Margin of error
- Bickel, Hammel & O’Connell (1975), sex bias in graduate admissions, Science 187
