Bayes formula:

Conditioning on a variable (useful if I don't know P(B) but know the stuff on the right side of the equation):

Problem

There are 10282 students at the university, out of whom 80 are on the 2nd year of Informatics. 50% of 2nd year Informatics students know Bayes theorem, out of the rest of the students 5% know it.

A student was randomly chosen and asked if they know the Bayes theorem. The answer was "Yes". Calculate the probability that this was a 2nd year Informatics student.

What are we looking for?

Random variables:

• IAIB3IAIB3 - student is 2nd year Informatics student (yes/no)
• KnowsBayesKnowsBayes - knows Bayes theorem (yes/no)

Need to find P(IAIB3=yes|KnowsBayes=yes)P(IAIB3=yes|KnowsBayes=yes)

First we need the initial data from the text. Use values in the range 0-1 to represent probabilities.

What is the value of P(KnowsBayes=yes|IAIB3=yes) given in the text?

Which of the following is not a Horn clause?

Which of the following matches best with the idea of symbolic reasoning?

The value function for A* is

Search strategy is...

It is the move of player "O" in position 1). The tree represents minimax search from the point of view of player "O".

For each level of the tree, decide if it's MAX or MIN level. Is the level with positions 5-10 a MIN or MAX level?

What is the best move from the starting position?

Compute the value of each position, using win=1, draw=0, loss=-1. Move upwards from leaves and take min() or max() of children.

What is the value of position 4?

It is the move of player "O" in position 1). The tree represents minimax search from the point of view of player "O".

For each level of the tree, decide if it's MAX or MIN level. Is the level with positions 5-10 a MIN or MAX level?

We have a simplified road map of Romania. Length of each road segment is shown.

Problem: find the path from S (Sibiu) to B (Bucharest).

We will use A* search. We need a heuristic function, for that we can use the distance of each point from the goal Bucharest:

Simulate the steps of the A* search with pen and paper (or a spreadsheet). The following table will help:

Then follow the algorithm:

1. select the row from the table with lowest f(n) that you haven't used yet. Mark it as "used".
2. If on this row the last city is "B" then the row contains the solution and its path length.
3. if it's not, find the cities you can move to from the last city. Add a row for each of these neighbor nodes to the table

Table after adding the neighbors of the initial state: