# 4.8 Probability topics: summary of formulas

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This module provides a review of the probability formulas, including the definitions of independent, complementary, and mutually exclusive events as well as the addition and multiplication rules.
Formula

## Complement

If $A$ and $\mathrm{A\text{'}}$ are complements then $\mathrm{P\left(A\right)}+\text{P(A' )}=1$

Formula

$\text{P(A OR B)}=\text{P(A)}+\text{P(B)}-\text{P(A AND B)}$

Formula

## Mutually exclusive

If $A$ and $B$ are mutually exclusive then $\text{P(A AND B)}=0$ ; so $\text{P(A OR B)}=\text{P(A)}+\text{P(B)}$ .

Formula

## Multiplication rule

• $\text{P(A AND B)}=\text{P(B)}\text{P(A|B)}$
• $\text{P(A AND B)}=\text{P(A)}\text{P(B|A)}$
Formula

## Independence

If $A$ and $B$ are independent then:

• $\text{P(A|B)}=\text{P(A)}$
• $\text{P(B|A)}=\text{P(B)}$
• $\text{P(A AND B)}=\text{P(A)}\text{P(B)}$

## Conditional probability

The likelihood that an event will occur given that another event has already occurred.

## Contingency table

The method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other. The table provides an easy way to calculate conditional probabilities

## Equally likely

Each outcome of an experiment has the same probability.

## Event

A subset in the set of all outcomes of an experiment. The set of all outcomes of an experiment is called a sample space and denoted usually by S. An event is any arbitrary subset in S. It can contain one outcome, two outcomes, no outcomes (empty subset), the entire sample space, etc. Standard notations for events are capital letters such as A, B, C, etc.

## Experiment

A planned activity carried out under controlled condition.

## Independent event

The occurrence of one event has no effect on the probability of the occurrence of any other event. Events A and B are independent if one of the following is true:
(1). P (A | B) = P (A)
(2). P (B | A) = P (B)
(3). P (A and B) = P (A) P(B)

## Mutually exclusive

An observation cannot fall into more than one class (category). Being in more than one category prevents being in a mutually exclusive category.

## Outcome

A particular result of an experiment.

## Probability

A number between 0 and 1, inclusive, that gives the likelihood that a specific event will occur. The foundation of statistics is given by the following 3 axioms (by A. N. Kolmogorov, 1930’s): Let S denote the sample space and A and B are two events in S . Then:
(1). 0≤P(A)≤1
(2). If A and B are any two mutually exclusive events, then P(A or B)= P(A)+P(B)
(3). P(S)=1

## Sample space

The set of all possible outcomes of an experiment.

## Tree diagram

The useful visual representation of a sample space and events in the form of a “tree” with branches marked by possible outcomes simultaneously with associated probabilities (frequencies, relative frequencies).

## Venn diagram

The visual representation of a sample space and events in the form of circles or ovals showing their intersection.

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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