### Gambling at Monte Carlo

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

### 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?

### 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?

# Jewellery Boxes

##### Stage: 4 Short Challenge Level:

Suppose that initially the total value of the jewels in $P$ is $£A$, and those in $Q$ is $£B$.

The average value in $P$ at the start is $\frac A3$. After the jewel has been moved it is $\frac{A-5000}2$. Therefore:

\frac A3 = \frac{A-5000}2 - 1000

Multiplying by $6$ and collecting like terms gives $A = 21000$.

The average value in $Q$ at the start is $\frac B3$. After the jewel has been moved, the average value is $\frac{B+5000}4$. Therefore:

\frac B3 = \frac{B+5000}4 - 1000

Multiplying by $12$ and collecting like terms gives $B = 3000$.

Therefore the total value is $£24,000$

This problem is taken from the UKMT Mathematical Challenges.