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There are **23** NRICH Mathematical resources connected to **Combining probabilities**, you may find related items under Probability.

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
### 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 Better Choice

Here are two games you can play. Which offers the better chance of winning?

Age 14 to 16

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
### 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
### Knock-out

Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?

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
### Odd Dice

These strange dice are rolled. What is the probability that the sum obtained is an odd number?

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
### Chance Combinations

Can you design a bingo board that gives you the best chance of winning?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dicey Decisions

Can you devise a fair scoring system when dice land edge-up or corner-up?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Molecular Sequencer

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Heavy Hydrocarbons

Explore the distribution of molecular masses for various hydrocarbons

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Taking Chances

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Taking Chances Extended

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Voting Paradox

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

Age 14 to 18

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
### Win or Lose?

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Marbles and Bags

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gambling at Monte Carlo

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

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