1. Basic knowledge

1.1. LAPLACE LAW

1.2. DEFINE USING YOUR TEXTBOOK:

· CASE.

· SAMPLE SPACE S.

· EVENTS.

2. Simple random experiments

2.1. Exercise

2.2. Exercise

2.3. Exercise

3. Frequency table

3.1. Exercise

The students of 3ºB are distributed like this:

	Girls	Boys
Wearing glasses	7	1
Not wearing glasses	10	2

We choose one student randomly.

• Calculate the probability of being girl.

• Calculate the probability of wearing glasses.

• Calculate the probability of not wearing glasses.

• Calculate the probability of being girl that wears glasses.

4. Event operations

4.1. Exercise

In the experiment that consists of drawing a card from a Spanish deck, the following events are considered: A = "Get out an ace" B = "Get out a glass" C = "Get out a king" D = "Get out a figure"

· Indicates which of them are compatible and which are incompatible.

· Find the probability of each of them.

4.2. Exercise

In the experiment that involves drawing a French deck card, the following events are considered: A = "Get an ace out" B = "Get out the three of spades" C = "Get out a king" D = "Get out a figure" E = "Get an 8 or a 9 or a 10".

Find the probability of each of them.

5. Opposite or complementary event

5.1. Exercise

In a small forest there are only 60 pines and 50 fir trees. If a tree is chosen at random, what is the probability that it is pine? And that it is fir trees? What is the relationship between both probabilities? How much do they add up?

6. Doing one test without studying

6.1. Do a random test.

Imagine that you don't know how to do anything and you decide to risk it. The test does not discount if there are errors. Calculate the probability of obtaining one 10. Calculate the probability of obtaining one 0 in this test.

7. On the calculator ...

Both calculators and computers have a chance function that is activated by pressing the RAND, RAN, or RANDOM key. Every time we press this key, we obtain a random number, called a random number, which is a decimal number between 0 and 1. Thus, by pressing the mentioned key ten times, we can obtain a different list from the one obtained by another partner. With the help of random numbers, we can simulate any type of random experiment without having to do it.

7.1. Examples:

• Throw a coin. If it is between 0 and 0.5 it is expensive. If it is between 0.5 and 1 it is tails.

• Raffle among 10 friends to see who's playing. If it is between 0 and 0.1, it is the first, if it is between 0.1 and 0.2, it is the second, etc. Etc.

• Simulate a 6-sided die. If it is between 0 and 1/6 it is a 1, if it is between 1/6 and 2/6 it is a 2, if it is between 2/6 and 3/6 it is a 3, if it is between 3/6 and 4/6 it is a 4, if it is between 4/6 and 5/6 it is a 5, if it is between 5/6 and 6/6 = 1 it is a 6.

• In a video game. If it is between 0 and 0.25 it goes up, if it is between 0.25 and 0.5 it goes to the right, if it is between 0.5 and 0.75 it goes to the bottom, if it is between 0.75 and 1 it goes to the left.

7.2. Exercise

Describe a random experience in which you would use random numbers with the calculator and how you would do it.

8. Games of chance.

8.1. La Primitiva

When playing La Primitiva, the Lottery or the pools, we think that it is possible and even probable that we will win the prize. It is actually possible, but very unlikely.

For example, playing a bet on La Primitiva we have a chance among almost fourteen million that it will touch us.

To calculate the number of bets that can be made on a Primitive:

There are the factorial numbers that are denoted like this: 4! And they are calculated by multiplying and going down to one: 4! = 4 * 3 * 2 * 1 = 24. With that rule 5! = 5 * 4 * 3 * 2 * 1 = 120.

To calculate the combinations that can be made there are combinatorial numbers. You have to put 49 boxes and 6 that are filled: which are approximately 14 million bets. If you made all the bets, it would be your turn, but you would spend 14 million euros and receive less of a prize. It is not profit.

The probability of hitting is 1 bet you play / 14000000 = 0.0000000714

8.2. La Quiniela

Playing a column in LA QUINIELA pool we have a chance among more than seventy-six million to get the full by 15.

To calculate it, we have 14 matches with 1 (home win) X (tie) 2 (visitor win) to score. This is 3 ^ 14 bets = 4,782,969. Over 4 million different ways to mark it. Then you have to put the plenary at fifteen, which are now 4 possibilities in two games. Then I multiply by 4 twice: total number of bets = 4 782 969 * 4 * 4 = 76 527 504

The probability of hitting a pool is 1 bet / 76 527 504 = 0.0000000131

Unlike the primitive, match forecasts are marked and not all teams are the same.

9. Other Spanish or European lotteries

9.1. Exercise

CALCULATE THE CHANCE OF BEING GRATEFUL IN THE FOLLOWING PRIZES

9.1.1. Christmas Lottery: With the Gordo.

9.1.2. ONCE Lottery: With the number+serial.

9.1.3. National Lottery: With the complete number.

9.1.4. EuroMillions

Research. Calculate the probability that you win EuroMillions.

10. PROBABILITY OF EVENTS FAIL-FAIL-FAIL-… -FAIL-SUCCESS

10.1. Exercise

Imagine that you are playing Parcheesi and you have to throw. Find the probability of rolling two sixes in a row and another number to avoid going home.

10.2. Exercise

Imagine that you throw darts, and your probability of hitting the target is 0.1. Find the probability of hitting the third attempt.

10.3. Exercise

Imagine that you are going to hunt. You have good aim. Your probability of hitting the hare is 0.6. Find the probability of a target on the fourth try.

10.4. Exercise

Imagine that you are going to hunt. You have bad aim. Your probability of hitting the partridge is 0.2. Find the probability of a target on the fourth try.

10.5. Exercise

Imagine taking a card out of the Spanish deck and putting it back in the deck. Find the probability of extracting the ace of gold.

10.6. Exercise

Imagine taking a card out of the French deck and putting it back in the deck. Find the probability of extracting the three of hearts.

10.7. Exercise

Imagine pulling a card from the French deck without Jokers and putting it back in the deck. Find the probability of extracting a figure J or Q or K.

10.8. Exercise

Imagine you toss a coin until it comes out heads. You roll 6 times. Find the probability of obtaining it at the sixth.

11. PROBABILITY OF EVENTS FAIL-FAIL-FAIL-… -FAIL OR SUCCESS-SUCCESS ... - SUCCESS

11.1. Exercise

Calculate the probability of drawing three six in a row on the parcheesi and going home.

11.2. Exercise

Find the probability of not rolling any six in four rolls of a dice.

11.3. Exercise

You are playing bullseye with darts. Bull eye's probability (50 points) is 0.1. Find the Bull Eye probability three times in a row.

11.4. Exercise

Your probability of hitting the target and scoring is 0.7. Find the probability of shooting three times and not scoring.

11.5. Exercise

Calculate the probability of drawing three figures in a row from a French deck J Q or K with replacement, that is, you draw the card and put it back in the deck.

11.6. Exercise

Calculate the probability of drawing three figures in a row from a French deck J Q or K without replacement, that is, you draw the card and do not put it back. Therefore, you have to figure the first, having 52 cards, the second, having 51 and the third having 50 cards.

12. THE FRENCH ROULETTE IN THE CASINO

The roulette mechanism is made up of a hollow cylinder with a conical base in which there are 37 sections numbered from 0 to 37, as if it were a clock, following a pattern elaborated by the Frenchman Blaise, creator of the original roulette and from which derived French Roulette and American Roulette.

12.1. Simple bets

• Even or odd:

This is the bet on all the odd or even numbers on the board, excluding 0.

Red or Black:

• This is the bet on all the red or black numbers on the board, excluding 0 which is green.

12.2. Calculate the following probabilities.

• Find the probability of odd.

• Find the probability of red.

• Find the probability of black.

12.3. Exercise

Imagine that you play your 10 chips one by one, always at even. What is the probability of winning the 10 times? What is your expected chips balance at the end of the 10 attempts?

12.4. Exercise

Imagine that you play your 100 chips one by one, always in red. What is the probability of winning the 100 times? What is your expected chips balance at the end of the 100 attempts?

12.5. A method to always win in the casino...

If you play in binary bets (odd / even), (red / black) ... doubling the amount until you win, you will surely win a chip.

Example: You always play even.

1. You bet a chip. It goes out even for the first time. You double. They give you two back. Since you played one, so you win one.

2. Odd I comes out, you lose a chip, you bet two chips again and it comes out even. You double, they return four, but since you bet two and lost one, so you win one.

3. Odd comes out I, you lose a chip, you bet two chips again and it comes out odd. You bet 4 chips again now. You double, eight are returned, but since you bet one two and four, so you win one.

4. … You always win one.

And why if you have the masterful method to become rich, you do not use it?

Because it only works when the binary bets are equiprobable and complementary (probability of even = probability of odd = 0.5 and 0.5 + 0.5 = 1). The presence of 0 breaks the system. The average mean of your money is negative. You could demonstrate with progressions easily.

And if there is no 0, the one who watches over the interests of the Casino, the croupier will interrupt your strategy.

Do you think that the casino was created to make you rich? Or to the casino?

13. COMPOUND EVENTS. RESOLUTION WITH TREE DIAGRAMS

13.1. Exercise:

A class consists of six girls and 10 boys. If a committee of three is chosen at random, find the probability of:

• 1 Select three boys.

• 2 Select exactly two boys and one girl.

• 3 Select exactly two girls and a boy.

• 4 Select three girls.

Build the diagram, based on the options and the probabilities of each.

13.2. Exercise:

Toss three coins:

• Calculate the probability that by tossing three coins, we get 3 heads:

• Calculate the probability that by tossing three coins, we get 2 heads:

• Calculate the probability that by tossing three coins, we get 1 heads:

• Calculate the probability that by tossing three coins, we get 3 tails: