Pokemon Hack Roms Mac

Bad Luck Strikes Again, Probability: Statistics for Dummies 6

Today is again Tuesday, 13 ... is it about the month of February, just weeks left to be four days of the week of March as February. But at least I hope that after the last chapter of ye likely more comfortable with the matter of bad luck.

Earlier chapters of Statistics for Dummies

Today we continue a little more likely, but for this we will return to school. In Class E there are many children, and each has their tastes. The teacher of the class E has a list of all the children and their tastes, not to be a mess with them.

Name	Boy or girl	Would you like football?	Do you like math?	Would you like lentils?
Juan	Child	Yes	not	Yes
Mary	Niña	not	If	If
Pedro	Child	If	If	not
Javier	Child	If	not	not
Marta	Niña	not	No	not
Sandra	Niña	not	If	If
Eduardo	Child	If	If	If
Beatriz	Niña	not	not	If

Well, these data have been filled thoughtlessly ... (Not There is no sexist connotation, is just one example)

The teacher of the class E is thinking of ways to sort the children in your class in groups for different activities. To do this, take this list, pencil and paper, and begins to make different groups:

Class E (all children): {John, Mary, Peter, Javier, Marta, Sandra, Eduardo, Beatriz }

Group of Children: {John, Peter, Javier, Eduardo}

Girls Group: {Mary, Martha, Sandra, Beatriz}

Let one thing, if we choose a random student, how likely is it child?

P (Child) = (number of children) / (number of students in the class E) = 0.5

And that's a girl?

P (girl) = (number of girls) / (number of students in the class E) = 0.5

And it is a student in the class E?

P (E) = (number of students) / (number of students) = 1

And the probability of an alien?

P (alien) = (number of aliens) / (number of students in the class E) = 0

What we get from here? Consider, first, the probability of choosing any student in the class E, is 1. The probability of choosing something that does not exist in the class E is 0. Put another way. The probability of E is 1, and "no E "is 0.

This "no-E" is usually expressed as E ^c (or contrary to E). The "against" can apply to other events. For example, if you like football, we can say is Football ^c . There is a property that the probability of something and its opposite, is always 1.

Here:

lentils Group: {John, Mary, Sandra, Eduardo, Beatriz}

Probability of choosing a student who likes lentils

P (lentils) = 5 / 8 = 0,625

Group who does not like lentils (or lentils c) : {Pedro, Javier, Marta}

P (lentils c) = 3 / 8 = 0,375

Group who likes lentils more the group does not like lentils: {John, Mary, Sandra, Eduardo, Beatriz} and {Pedro, Javier, Marta}, {John, Mary, Sandra, Eduardo, Beatriz, Pedro, Javier, Marta}: All Class E

P (lentils) + P (lentils c) = 0,625 + 0,375 = 1

addition, there is another ownership. How many children will be common in both groups? If you look, none.

Well, this can define a concept:

is said that two events are INCOMPATIBLE , when the probability of of one plus the probability of another, is equal to 1 (the entire sample space) and the probability of finding a common element in the two events is 0. Are said to COMPATIBLE when it is not given.

addition, we define two basic operations in probability:

UNION (U) is the operation where we take the two lists and unite. The probability P (AUB) means the probability of the event A or event B

INTERSECTION (∩) is the operation that allows us to learn how many common elements are the two lists. The probability P (A ∩ B) is the probability of A and B.

For two compatible events, for example, the list of students who likes soccer and lentils:

Football: {John, Peter, Javier, Eduardo}

Lentils: {John, Mary, Eduardo, Beatriz}

In many students likes football and lentils

Football Lentils ∩ {John, Eduardo}

How many students would like football or lentils: Football

U Lentils: {John, Peter, Javier, Eduardo} + {John, Mary, Eduardo, Beatriz} = {Juan, Pedro, Javier, Eduardo, Juan, Maria, Eduardo, Beatriz}

But John and Eduardo are repeated ... why football is subtracted ∩ Lentils:

Football

U Lentils: Lentils Group Football + Group - Group (∩ Football Lentils) = {Juan, Pedro, Javier, Eduardo} + {John, Mary, Eduardo, Beatriz} - {Juan, Eduardo} = {John, Peter, Eduardo, Maria, Beatriz}.

words:

P (AUB) = P (A) + P (B) - P (A ∩ B).

If the events are inconsistent, the term P (A ∩ B) will be worth 0, so that will be like adding the probabilities of each event.

Here's another thing. First place the list of lentils and then football is the same as putting on football first and then the lentils. It is what is called commutative.

Football: {John, Peter, Javier, Eduardo}

Lentils: {John, Mary, Eduardo, Beatriz}

Football U U Football Lentils Lentils =

Similarly :

Football ∩ ∩ Football Lentils Lentils =

There is also an attached property. That is,

U Lentils Football Football U = U Mathematics (Math U Lentils) =

(Football Lentils U) U Mathematics

Football Math = ∩ ∩ Lentils Football ∩ (∩ Lentils Math) =

(Football Lentils ∩) ∩ Mathematics

(I leave it to you to do this on your own if you fancy)

Well, today I think we have quite dizzy the teacher of the class E. And continue in other chapters with our friends in the class E.

A greeting

quantum

The black cat strikes again