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?
Which of these games would you play to give yourself the best possible chance of winning a prize?
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .
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. . . .
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?
A maths-based Football World Cup simulation for teachers and students to use.
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.
So which is the better bet? Both games cost £1 to play.
Getting two heads and two tails for £3 or £2 for every
six when three dice are rolled.
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 ?
When five dice are rolled together which do you expect to see more
often, no sixes or all sixes ?
How could you compare different situation where something random
happens ? What sort of things might be the same ? What might be
A weekly challenge concerning combinatorical probability.
Can you work out the probability of winning the Mathsland National
Lottery? Try our simulator to test out your ideas.
What is the chance I will have a son who looks like me?
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?
If everyone in your class picked a number from 1 to 225, do you
think any two people would pick the same number?
Can you work out which spinners were used to generate the frequency charts?
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
Calculate probabilities associated with the Derren Brown coin scam
in which he flipped 10 heads in a row.
Imagine a room full of people who keep flipping coins until they
get a tail. Will anyone get six heads in a row?
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!
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
A man went to Monte Carlo to try and make his fortune. Whilst he
was there he had an opportunity to bet on the outcome of rolling
dice. He was offered the same odds for each of the. . . .
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?
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. . . .
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?
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?
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
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.
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. . . .
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?
This set of resources for teachers offers interactive environments
to support probability work at Key Stage 4.
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.
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?
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.
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. . . .
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
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.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
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