You may also like

problem icon

Gambling at Monte Carlo

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

problem icon

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?

problem icon

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?

Marbles and Bags

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

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags (it is not known from which bag). The marble is blue. What is the probability that it was removed from bag A?

Bag A

2 RED

3 BLUE

Bag B

3 RED

4 BLUE


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2017. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.