0. Before you get to work, you have to send me a mail regarding the statistics project. Specify name of the team, members of the group, and an initial idea of the topic.

Now it’s time to get into combinatorics:

1. First, the basic counting principle: the rule of product. Read this and solve the questions.

1. Read this page and solve the questions at the end.

2. Now some problems. Solve them in a word document. If needed, draw tree diagrams (you can use “autoformas”, see this tutorial . Or use Geogebra and paste the drawing). Send me the file, of course.

- A box has 8 red balls, 5 yellow and 7 green. If a ball is extracted at random, calculate the probability that it will be:

Red.

Green.

Yellow.

Not red.

Not yellow.

-A box contains three red balls and seven blue. Two balls are drawn at random. Define the sample space and find the probability of events when:

The first ball is replaced before the second is drawn.

The first ball is not replaced before the second is drawn.

-A ball is drawn from a box containing 4 red balls, 5 blue and 6 green. What is the probability that the ball will be red or white? What is the probability that it is blue? If you take out another ball, what are the chances of being red?

3. And now practice with this really large worksheet. Send me the two most interesting problems (the ones you think should be in the exam).

1) Choose the dice. The game is a simulation of the rolling of two dice. Play a little with it and answer these questions?

a) Which results are more and less likely?

b) What are the theoretical probabilities of each result? Make a diagram to solve this question.

2) Now we are going to create a couple of very basic simulations with Geogebra. Pay attention, because the tools you are going to see are quite useful. Send me the files at the end.

First of all, take a look at the “Olimpiadas matemáticas” thing, and tell me if you wanna take part.

Today we are going to learn the basic vocabulary of probability. (NOTE: you will need the last part of the book for the rest of the course, bring it tomorrow)

1. Go to this page and try to find all the most important concepts. Write them in a glossary, with their spanish equivalence.

For example:>> Sample space=Espacio muestral

2. There are more of these words in this page. You can find the spanish equivalences in this page.

3. Send me this glossary.

4. Now solve these questions. Use your notebook. The key to solve most of them is Laplace’s rule.

5. Now some problems. Solve them in a word document. Send me the file, of course.

- A box has 8 red balls, 5 yellow and 7 green. If a ball is extracted at random, calculate the probability that it will be:

Red.

Green.

Yellow.

Not red.

Not yellow.

-A ball is drawn from a box containing 4 red balls, 5 blue and 6 green. What is the probability that the ball will be red or white? What is the probability that it is blue? If you take out another ball, what are the chances of being red?

-In a class there are 10 blonde girls, 20 brunette girls, 5 blonde boys and 10 brown-haired boys. If all 45 students attend class on a particular day, find the probability that a student selected at random will be:

A boy.

A brunette girl.

A boy or girl.

If the student is a boy, find the probability that he’s blonde.

If the student is brown-haired, find the probability that she’s a girl.

-A die is rigged so that the probabilities of obtaining the different faces are proportional to the numbers on the faces (For example: A five is five times more likely to be rolled than a one). Find:

Some exercises from vitutor.com to do before the exam. You should solve them FIRST in your NOTEBOOK, and correct them with the computer (but who am I to give you advice?).

1. Vectors: (Solve the sections anotated in parenthesis):