The Birthday Bet
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.
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Coin Tossing Games
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?
Fixing the Odds
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?
Penta Colour
In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?