### Football World Cup Simulation

A maths-based Football World Cup simulation for teachers and students to use.

### Winning the Lottery

Try out the lottery that is played in a far-away land. What is the chance of winning?

### In the Playground

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

# Probably ...

##### Stage: 2 Challenge Level:

We've received a large number of good responses to this problem.

Alex, Chris, Alastair and Henry from St Peter's College and Emmy gave a comprehensive response to the problem:

Statement: $6$ is the hardest number to throw on a dice.
Response: $6$ is not the hardest number to throw on a dice, it has an equal chance of being thrown as all the other numbers from $1$-$6$

Statement: A game is fair if you play it properly.
A game is not always fair if you play it properly.  In sport, the umpires could favour a losing team because they were getting demolished.  If the winning team is playing properly, then it is not always fair.

Statement: I will see someone I know on the way home from school.
People do sometimes see people on the way home from school, it can happen. If you live right next to someone from your school, the chances are better than if you live $1000$ miles away. Also, if you catch a school bus, the chances are 100%.

Statement: It always rains in the summer holidays.
It doesn't always rain in the summer holidays, but the chances are very high as it is a very long period.

Statement: If you buy lots of raffle tickets, you're sure to win a prize.
If you buy lots of raffle tickets you are not assured of winning a prize, it just increases your chances. The only way to assure yourself of winning a prize is cheating :) or buying all of the raffle tickets.

Statement: It's easier to get heads than tails when you flip a coin.
Yes, it is easier to get heads rather then tails on a coin flip because the tails side of a coin is heavier than the heads side, this marginly increases you chances, but not by much.

I am not sure about the response to the last statement ...  What's your evidence for this, I wonder?!

Gabriel and Oscar from St Saviours CE Primary School also sent a great response using interesting examples demonstrating their point:

We disagree with all the statements.

Statement: A game is fair if you play it properly

In the England v Germany game in the World Cup 2010, Frank Lampard scored and everyone was playing properly, but the referee didn't see the goal so the goal wasn't allowed. This wasn't fair, but everyone was playing properly.

Statement: 6 is the hardest number to throw on a dice.
There are an equal number of each number on the dice so there is a one in six chance of rolling any number.

Statement: I will see someone I know on the way home from school.
If you were blind you wouldn't see anyone on your way home and if you were in a taxi and you fell asleep you wouldn't see anyone until you were at home.

Statement: It always rains in the summer holidays.
It depends where you are living in the summer. For example if you lived in Libya, it wouldn't rain. Or if your holidays were only short, there would be a smaller chance of rain because there would be less days for it to rain on.

Statement: If you buy lots of raffle tickets, you're sure to win a prize.
There would be a bigger chance of winning but you couldn't be sure of anything.

Statement: It's easier to get heads than tails when you flip a coin.
There is a 50% chance of getting either heads or tails because there is one of each.