## Exercise 1: Bertrand’s Box

Consider the following problem (known as the Bertrand’s box paradox).

There are three boxes:

- a box containing two gold coins,
- a box containing two silver coins,
- a box containing one gold coin and a silver coin.

We first select a box at random, and then we pick a coin at random from this box.
If this coin is gold, what is the probability that the second coin is also gold?

Model and solve this problem.

## Exercise 2: character sequences

We have a process that generates random sequences consisting of the characters `a`

, `b`

, and `c`

.
These characters have probability 0.4, 0.2 and 0.1, respectively.
With probability 0.3 the sequence ends.

- What is the probability of the sequence
`a, b, a`

?
- What is the probability that a sequence of length 4 is generated?
- What is the probability that a sequence of length 4 has a
`b`

in the second position?

%
seq(N, ['$']) :- ....
seq(N, [H|T]) :-
...
N1 is N + 1,
seq(N1, T).
seq(S) :- seq(0, S).
...
%