Invent a set of three dice where each one is better than one of the
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. . . .
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 ?
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 the probability of winning the Mathsland National
Lottery? Try our simulator to test out your ideas.
Use cunning to work out a strategy to win this game.
How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
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. . . .
Explore these X-dice with numbers other than 1 to 6 on their faces.
Which one is best?
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?
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?
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?
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
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.
In how many different ways can I colour the five edges of a
pentagon red, blue and green so that no two adjacent edges are the