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### Number and algebra

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### For younger learners

### Advanced mathematics

# In a Box

## You may also like

### Gambling at Monte Carlo

### Marbles and Bags

### Coin Tossing Games

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Age 14 to 16

Challenge Level

Chris and Jo decide to play a game.

They put some red and some blue ribbons in a box.

They each pick a ribbon from the box without looking (and without replacing them).

Jo wins if the two ribbons are the same colour and Chris wins if the two ribbons are a different colour.

**How many ribbons of each colour would you need in the box to make it a fair game?**

**Is there more than one way to make a fair game?**

*This problem is based on one offered by Doug Williams at the 2003 ATM conference in Bath UK. See also http://www.blackdouglas.com.au/taskcentre*

Click here for a poster of this problem.

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

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?

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?