There are 67 NRICH Mathematical resources connected to Theoretical probability, you may find related items under Probability.Broad Topics > Probability > Theoretical probability
What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you work out which spinners were used to generate the frequency charts?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
The next ten people coming into a store will be asked their birthday. If the prize is £20, would you bet £1 that two of these ten people will have the same birthday ?
Here are two games you have to pay to play. Which is the better bet?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Are these games fair? How can you tell?
Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?
Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!
Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.
After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?
Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.
Which of these games would you play to give yourself the best possible chance of winning a prize?
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.
It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?
Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?
Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
What do we mean by probability? This simple problem may challenge your ideas...
This article offers an advanced perspective on random variables for the interested reader.
Can you design your own probability scale?
How do you describe the different parts?
What are the likelihoods of different events when you roll a dice?
When two closely matched teams play each other, what is the most likely result?
A problem about genetics and the transmission of disease.
Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?
Engage in a little mathematical detective work to see if you can spot the fakes.
You'll need to work in a group for this problem. The idea is to decide, as a group, whether you agree or disagree with each statement.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
What is the chance I will have a son who looks like me?
A weekly challenge concerning combinatorical probability.
Calculate probabilities associated with the Derren Brown coin scam in which he flipped 10 heads in a row.
By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?
How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?
Which of these ideas about randomness are actually correct?
Can you generate a set of random results? Can you fool the random simulator?
Think that a coin toss is 50-50 heads or tails? Read on to appreciate the ever-changing and random nature of the world in which we live.
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
Heads or Tails - the prize doubles until you win it. How much would you pay to play?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first?