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There are 127 NRICH Mathematical resources connected to Probability, you may find related items under Probability.Broad Topics > Probability > Probability
In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
When two closely matched teams play each other, what is the most likely result?
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?
Engage in a little mathematical detective work to see if you can spot the fakes.
What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Can you work out the probability of winning the Mathsland National Lottery?
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
The class were playing a maths game using interlocking cubes. Can you help them record what happened?
Is the regularity shown in this encoded message noise or structure?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you work out which spinners were used to generate the frequency charts?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Is the age of this very old man statistically believable?
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
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 ?
Here are two games you can play. Which offers the better chance of winning?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Are these domino games fair? Can you explain why or why not?
Are these games fair? How can you tell?
Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?
Play this dice game yourself. How could you make it fair?
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?
In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!
Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.
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?
Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.
Which of these games would you play to give yourself the best possible chance of winning a prize?
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?
Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.
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?
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?
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.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
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?
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?
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?
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?
A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?
A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?
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?