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?
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?
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
Here's a puzzle :
The next ten people coming into a store will be asked what day in the year their birthday is. For example 17th October.
If the prize is £20, would you bet £1 that two of these ten people will have the same birthday ?
If not, what's the lowest prize value for which you would take this bet and why?
No matter how big the prize or how easy it looks to win, it isn't smart to bet if I can't stand the loss.
However, lots of things are not certain and we often need to make decisions in the face of that uncertainty.
Probability is how mathematicians quantify uncertainty.
Puzzles and games can be an excellent way to explore this.