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Broad Topics > Probability > Conditional probability

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 ?

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?

Put Out

Stage: 5 Challenge Level:

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?

In a Box

Stage: 4 Challenge Level:

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Snooker Frames

Stage: 5 Challenge Level:

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

Rain or Shine

Stage: 5 Challenge Level:

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

Statins and Risk

Stage: 4 Challenge Level:

"Statins cut the risks of heart attacks and strokes by 40%"
Should the Professor take statins? Can you help him decide?

How Risky Is My Diet?

Stage: 3 and 4 Challenge Level:

Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

Non-transitive Dice

Stage: 3 Challenge Level:

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

Drug Testing

Stage: 5 Challenge Level:

How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?

Ante Up

Stage: 5 Challenge Level:

Use cunning to work out a strategy to win this game.

At Least One...

Stage: 3 Challenge Level:

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

Mathsland National Lottery

Stage: 4 Challenge Level:

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

Same Number!

Stage: 4 Challenge Level:

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Dicey Dice

Stage: 5 Challenge Level:

Invent a set of three dice where each one is better than one of the others?

X-dice

Stage: 5 Challenge Level:

Explore these X-dice with numbers other than 1 to 6 on their faces. Which one is best?

Succession in Randomia

Stage: 5 Challenge Level:

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

Master Minding

Stage: 3 Challenge Level:

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

Penta Colour

Stage: 4 Challenge Level:

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 same colour?

Fixing the Odds

Stage: 4 Challenge Level:

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. . . .

Coin Tossing Games

Stage: 4 Challenge Level:

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. . . .

Snooker

Stage: 5 Challenge Level:

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Squash

Stage: 5 Challenge Level:

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?