### 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?

# Two Girls

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

Let the number of boys in the class be $x$.

Hence $\frac{10}{10+x}\times\frac{9}{9+x} = 0.15 = \frac{3}{20}$.

Simplifying gives $1800=3(10+x)(9+x)$ and then $x^{2}+19x-510=0$.

Factorising gives $(x+34)(x-15)=0$ and, since $x\not=-34$, $x=15$.

Alternatively, let the number of students in the class be $x$.

Hence $\frac{10}{x}\times\frac{9}{x-1} = 0.15 = \frac{3}{20}$.

Simplifying gives $600=x(x-1)$ and then $x^{2}-x-600=0$.

Factorising gives $(x+24)(x-25)=0$ and, since $x\not=-24$, $x=25$.

Therefore the number of boys in the class is 15.

Students from Comberton Village College sent us these solutions.

This problem is taken from the UKMT Mathematical Challenges.