Indiana University CSCI-B 551

Now you roll the red and white dice. What is the probability that at least one die is 5, given that the sum of the dice is an odd number?

1/3

Now you roll all three dice. What is the probability that all three show the same number?

1/36

You have a red die, a white die, and a blue die. The red and white dice are "fair" in that the probability of any given number being rolled is one-sixth. The blue die is biased so that the probability of rolling a 1 is one-half while the probability of rolling each of the other numbers is one-tenth. You roll the red and white dice. What is the probability of rolling "snake eyes" (two ones)?

1/36

You have a red die, a white die, and a blue die. The red and white dice are "fair" in that the probability of any given number being rolled is one-sixth. The blue die is biased so that the probability of rolling a 1 is one-half while the probability of rolling each of the other numbers is one-tenth. You roll the red and white dice. What is the probability of rolling an odd number on the red die and an even number on the white die?

1/4

Now you roll all three dice. What is the probability that the sum of the red and blue dice is 7, given that the white die is odd?

1/6

At a certain carnival booth, people pay $1 to enter a game in which they roll a die and get paid $1 if they roll an even number and $2 if they roll a 5, and otherwise get paid nothing. On average, about how much does the carnival owner profit from each person who enters?

17 cents

Assuming a state graph with a branching factor of 10 and an optimal solution of path length 20, and a computer that can evaluate one trillion states per second, about how long would it take BFS to find the solution in the worst case?

3 years

You have a red die, a white die, and a blue die. The red and white dice are "fair" in that the probability of any given number being rolled is one-sixth. The blue die is biased so that the probability of rolling a 1 is one-half while the probability of rolling each of the other numbers is one-tenth. You roll the blue die. What is the probability of rolling an even number?

3/10

Now you roll the red and white dice. What is the probability that at least one die shows an even number?

3/4

Suppose we have a Bayes net with 5 variables, A, B, C, D, and E. Suppose that A is not connected to any other vertex in the graph. This implies that (check all that apply):

A is independent from all other variables in the network P(A,B,C,D,E) can be factored into P(A)P(B,C,D,E)

The major advantage of A* search (assuming an admissible and consistent heuristic function and supposing the cost function is uniform) over breadth first search is:

A* may find as good a solution as BFS, but with a shorter amount of computation time

An advantage of Breadth First Search over Depth First Search is that:

BFS is complete

The first chess computer to win a game against a reigning world champion (under regular time controls) was...

Deep Blue

Suppose you have code for a priority queue that supports two operations: insert(element, priority) and remove(). Remove is guaranteed to remove the element the lowest priority value currently in the priority queue. How would you implement a stack using this priority queue?

Keep a counter called N, initially at 0. Call insert(element, N), and decrement N by 1 after each call to insert().

https://iu.instructure.com/courses/1820689/files/92435237/preview Consider the state graph below, where costs are indicated by edge weights and the value of heuristic function h(s) is indicated next to each node. Is h(s) consistent?

No, because h(B)=10.

In practice, what is one main problem with building an AI that could beat a highly-skilled human player in chess?

Planning multiple moves ahead requires exploring a very large (exponential) state space.

Consider the same state graph above. Which of the following is one possible order in which A* will *remove* nodes from the fringe? Assume we are using Search Algorithm #2, so that duplicate states are not discarded.

S, A, B, C, D, G

If a spam classifier makes the Naive Bayes assumption, it is likely to underestimate:

The probability that the words "president" and "obama" both occur in a non-spam document.

A* is typically used to solve the 8-tile puzzle (in the fewest number of moves) instead of local search. Why?

We're trying to find the path to the goal, not the goal state itself. There are very effective admissible heuristic functions for the 8-tile puzzle.

https://iu.instructure.com/courses/1820689/files/92435267/preview Let's assume you are running the alpha-beta algorithm on the above game tree. Can you prune the right-side branch underneath the M node? Why or why not?

Yes, because beta = -2 is smaller than alpha = 4.

The fringe in Depth First Search can be implemented as:

a stack

I'll give you $10 if you roll a die 3 times and get at least one 1. How much should you expect to earn?

about $4.21

My friend Mary lies 20% of the time. She calls me and says that it's currently raining in Amsterdam. I know that at any given time, there's a 30% chance of rain in Amsterdam. What's the probability that it's really raining in Amsterdam?

about 60%

You roll three six-sided dice. Let A be the event that exactly one of the dice shows an odd number. Let B be the event that exactly one of the dice shows an even number. A and B: (mark all that apply)

are disjoint are equally probable

You roll a six-sided die three times in a row. Let A be the event that the first roll is odd. Let B be the event that the second roll is odd. A and B: (mark all that apply)

are independent are equally probable

Suppose you have an implementation of A* search, but you do not know a good heuristic function for your problem. Which of the following heuristic functions would guarantee finding an optimal solution using A* search?

h(s) = 0

A disadvantage of Iterative Deepening Search is that:

in a practical implementation, it is usually slower than Breadth First Search

Beam search:

is a generalization of local search that explores multiple promising states at once requires more memory than traditional local search may help prevent local search from getting "stuck" near states that appear promising but are not

The evaluation function e(s)... (check all that apply)

is a heuristic that estimates how favorable a state s is for MAX to win. is needed to plan a good move when you cannot explore the entire game tree.

A key property of Variable Elimination is that:

it can be used to solve any Bayes net, but may not do so efficiently

A major advantage of local search over A* search is:

it uses less memory

In the Student Bayes net we saw in the video, Difficulty and Intelligence are *not* conditionally independent given Grade because, for example:

knowing that you took hard classes and good grades means you're more likely to be intelligent

The key idea behind Variable Elimination is to "get rid of" one variable at a time by:

summing over all possible values of that variable

As a general rule of thumb, the more edges a Bayes net has... (check all that apply)

the fewer conditional independence assumptions it makes. the more computationally demanding it is to perform inference.

It's raining today, and I'd like to predict the probability that it will rain tomorrow. To apply Bayes' Law to this problem, I would need to know all of the following except:

the posterior distribution of rain tomorrow given rain today

The main idea behind Monte Carlo descent is:

to force local search to explore states that seem bad, because they may lead to much better states

The basic idea behind alpha-beta pruning is...

to take advantage of upper and lower bounds of propagated utility values.

Suppose you are trying to use gradient descent to minimize f(x,y), i.e. to find the values of x and y where f(x,y) is minimum, where: f\left(x,y\right)=x^2+yf ( x , y ) = x 2 + y Gradient descent is currently considering the state x=3, y=2. Which of the following states might it consider next?

x=0, y=1.5

Your friend proposes a heuristic function h(s) for a problem where the true cost to the goal is h*(s), but you are pretty sure it is not admissible. How could you prove this with the least effort?

Give an example of a state s for which h(s) > h*(s)