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In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
Can you decide whether these short statistical statements are always, sometimes or never true?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
When two closely matched teams play each other, what is the most likely result?
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.
Can you work out the probability of winning the Mathsland National Lottery?
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
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?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
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.
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
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 can play. Which offers the better chance of winning?
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?
Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?
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?
Explore the distribution of molecular masses for various hydrocarbons
How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?
In the time before the mathematical idea of randomness was discovered, people thought that everything that happened was part of the will of supernatural beings. So have things changed?
If a coin rolls and lands on a set of concentric circles what is the chance that the coin touches a line ?
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?
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?
The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.
Here are some examples of 'cons', and see if you can figure out where the trick is.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
This is a game for two players. Does it matter where the target is put? Is there a good strategy for winning?
All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.
A maths-based Football World Cup simulation for teachers and students to use.
In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?
Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?
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 corner of the grid?
Is a score of 9 more likely than a score of 10 when you roll three dice?
In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?
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?
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 bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?
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 he more money than he started with?
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 a head (you win). What is the probability that you win?
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?
A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?