Probability - November 2005, Stage 3&4

Problems

problem icon

Flippin' Discs

Stage: 3 Challenge Level: Challenge Level:1

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?

problem icon

Cosy Corner

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Two's Company

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Odds and Evens

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

problem icon

The Better Bet

Stage: 4 Challenge Level: Challenge Level:1

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.

problem icon

The Birthday Bet

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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 ?

problem icon

Bet You a Million

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.