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There are **26** NRICH Mathematical resources connected to **Conditional probability**, you may find related items under Probability.

Problem
Primary curriculum
Secondary curriculum
### Non-transitive Dice

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### At Least One...

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mathsland National Lottery

Can you work out the probability of winning the Mathsland National Lottery?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Same Number!

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Birthday Bet

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 ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two's Company

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Put Out

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In a Box

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Snooker Frames

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rain or Shine

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Do You Brush Your Teeth Every Day?

How can we find out answers to questions like this if people often lie?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dropouts

What percentage of students who graduate have never been to France?

Age 14 to 16

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Statins and Risk

"Statins cut the risks of heart attacks and strokes by 40%"

Should the Professor take statins? Can you help him decide?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Risky is My Diet?

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Drug Testing

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dicey Dice

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### X-dice

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Succession in Randomia

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Master Minding

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Snooker

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squash

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?

Age 16 to 18

Challenge Level