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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?
When two closely matched teams play each other, what is the most likely result?
Can you work out the probability of winning the Mathsland National Lottery?
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?
Is the regularity shown in this encoded message noise or structure?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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?
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?
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.
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?
Why MUST these statistical statements probably be at least a little bit wrong?
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 ?
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.
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?
A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.
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.
Playing squash involves lots of mathematics. This article explores the mathematics of a squash match and how a knowledge of probability could influence the choices you make.
Edward Wallace based his A Level Statistics Project on The Mean Game. Each picks 2 numbers. The winner is the player who picks a number closest to the mean of all the numbers picked.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
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.
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?
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?
A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?
If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?