Resources tagged with: Theoretical probability

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Broad Topics > Probability > Theoretical probability

Mathsland National Lottery

Age 14 to 16 Challenge Level:

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

Last One Standing

Age 14 to 16 Challenge Level:

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

The Random World

Age 11 to 18

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.

Taking Chances

Age 11 to 14 Challenge Level:

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.

Coin Tossing Games

Age 14 to 16 Challenge Level:

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by. . . .

Bet You a Million

Age 14 to 16 Challenge Level:

Heads or Tails - the prize doubles until you win it. How much would you pay to play?

The Birthday Bet

Age 14 to 16 Challenge Level:

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 ?

Same Number!

Age 14 to 16 Challenge Level:

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

A Probability Conundrum

Age 14 to 18

What do we mean by probability? This simple problem may challenge your ideas...

Taking Chances Extended

Age 14 to 18

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.

What Do You Know about Probability? (2)

Age 11 to 14 Challenge Level:

What are the likelihoods of different events when you roll a dice?

Age 11 to 14 Challenge Level:

Can you design your own probability scale?
How do you describe the different parts?

Misunderstanding Randomness

Age 11 to 14 Challenge Level:

Which of these ideas about randomness are actually correct?

Gambling at Monte Carlo

Age 14 to 16 Challenge Level:

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

Can't Find a Coin?

Age 11 to 14 Challenge Level:

Can you generate a set of random results? Can you fool the random simulator?

The Better Bet

Age 14 to 16 Challenge Level:

Here are two games you have to pay to play. Which is the better bet?

Odds and Evens

Age 11 to 14 Challenge Level:

Are these games fair? How can you tell?

Which Spinners?

Age 14 to 18 Challenge Level:

Can you work out which spinners were used to generate the frequency charts?

At Least One...

Age 11 to 14 Challenge Level:

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?

Who's the Winner?

Age 14 to 16 Challenge Level:

When two closely matched teams play each other, what is the most likely result?

Nine or Ten?

Age 11 to 14 Short Challenge Level:

Is a score of 9 more likely than a score of 10 when you roll three dice?

Age 11 to 14 Challenge Level:

Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.

Age 11 to 14 Challenge Level:

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path. . . .

Fixing the Odds

Age 14 to 16 Challenge Level:

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .

Win or Lose?

Age 14 to 16 Challenge Level:

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has. . . .

Marbles and Bags

Age 14 to 16 Challenge Level:

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

Distribution Differences

Age 14 to 16 Challenge Level:

How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?

Like Father Like Son

Age 14 to 16 Challenge Level:

What is the chance I will have a son who looks like me?

Interactive Spinners

Age 11 to 14 Challenge Level:

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Two's Company

Age 11 to 14 Challenge Level:

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Chances Are

Age 14 to 16 Challenge Level:

Which of these games would you play to give yourself the best possible chance of winning a prize?

Cosy Corner

Age 11 to 14 Challenge Level:

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Flippin' Discs

Age 11 to 14 Challenge Level:

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

What Does Random Look Like?

Age 11 to 14 Challenge Level:

Engage in a little mathematical detective work to see if you can spot the fakes.

Age 14 to 18 Challenge Level:

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

In a Box

Age 14 to 16 Challenge Level:

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?

Age 14 to 16 Challenge Level:

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

Genetics

Age 14 to 16 Challenge Level:

A problem about genetics and the transmission of disease.

Football World Cup Simulation

Age 7 to 16 Challenge Level:

A maths-based Football World Cup simulation for teachers and students to use.

Scratch Cards

Age 14 to 16 Challenge Level:

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?