Motto: Games and Probabilities
Assignment 4.1∗∗
Solve the Nim game, this time write a minimax algorithm for this purpose.
Assignment 4.2

Assuming that girls and boys are born with the same probability of 50%, and knowing that a family
has two children, one of which is a boy, what is the probability of the other child to be a boy, too?
Assignment 4.3
Consider a family with 5 children and the probability of a particular child being a boy or girl being

1. What is the probability that the family has one boy only?
2. What is the probability that the family has precisely two boys?
3. What is the probability that the family has precisely k boys?
4. What is the probability that the family has at least one boy?
5. What is the probability that the family has at least two boys?
6. (*) What is the probability that the family has at least k boys?
   Assignment 4.4∗
   Repeat the questions from Assignment 4.3, but now assuming a general number n of children.
   Assignment 4.5
   (do this only if you have covered minesweeper already) Solve the minesweeper problem for a different
   number of cells (begin with 4). This is a paper exercise. Write down the decision tree.
7. Begin with the initial state where you do not know anything (the probabilities for all mine
   positions are the same)
8. Choose a uncovering “move” according to the Bayes probability
9. Split the outcomes according to their probabilities
10. Carry out a Bayes update for each of the possibilities
11. Again, choose the best “move” (uncovering) for each these possibilities
12. etc., until the tree is complete
    Reference