# Probability - November 2005, All Stages

## Problems

### Three Ball Line Up

##### Stage: 1 Challenge Level:

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

### Domino Pick

##### Stage: 1 Challenge Level:

Are these domino games fair? Can you explain why or why not?

### Two and One

##### Stage: 1 Challenge Level:

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

### Odds or Sixes?

##### Stage: 2 Challenge Level:

Use the interactivity or play this dice game yourself. How could you make it fair?

### The Twelve Pointed Star Game

##### Stage: 2 Challenge Level:

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

### Flippin' Discs

##### Stage: 3 Challenge Level:

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

### Cosy Corner

##### Stage: 3 Challenge Level:

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

### Two's Company

##### Stage: 3 Challenge Level:

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

### Odds and Evens

##### Stage: 3 and 4 Challenge Level:

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

### The Better Bet

##### Stage: 4 Challenge Level:

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 Birthday Bet

##### Stage: 4 Challenge Level:

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 ?

### Bet You a Million

##### Stage: 4 Challenge Level:

Heads or Tails - the prize doubles until you win it. How much would you pay to play?

### Epidemic Modelling

##### Stage: 4 and 5 Challenge Level:

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

### Spinners

##### Stage: 5 Challenge Level:

How do scores on dice and factors of polynomials relate to each other?