# Critical Thinking E4

# Probability Wiki

+ **Probability**

Probability is the measure of our belief that something will happen. For example, there is a 1/2 chance that I will get a head when flipping a quarter. There is a 90% chance that I will go for a bike ride tomorrow morning.

- **Theoretical Probability**

you type here. to open a new line, hit enter at the end of a line, then indent the line

- **Empirical Probability**

An "estimate" that the event will happen based on how often the event occurs after collecting data or running an experiment. It is based specifically on direct observations or experiences. (Lauren Cagle)

- **Experts Opinion**

EWAG or best guess made on experience and technical knowledge (Pat Blaine)

+ **Minimum Probability**

+ **Maximum Probability**

+ **Experiment**

(Tate Spivey) An Experiment is a controlled test where the outcome is already pre-determined.

+ **Chance** (Lorasa Jodie)

possibility of something happening; the absence of any cause of events that can be predicted, understood, or controlled.

+ **Sample Space**

The set of all possible outcomes of an experiment. (Mike Derrickson)

+ **Outcome**

A particular result of an experiment. (Laura Jokinen)

+ **Event**

A subset of the set of all outcomes of an experiment. It may contain one outcome, two outcomes, no outcomes (empty subset), the entire sample space, and so on. Standard notation for Events are capital letters (A, B, C....). (Mike Derrickson)

+ **Simple Event**

A simple event is any one or more outcomes of a certain situation. (Rayne Spencer)

+ **Equally Likely**

All outcomes have an equal chance of happening. (Colin Wallace)

+ **Fair**

Any event has a equal probability of happening. A fair coin toss is when the coin has a equal probability of landing on either heads or tails.(Shyla Davison)

+ **Long-term Relative Frequency**

The probability of the occurrence of an event, in which a large number of repetitions are observed in the experiment. (Kyra Perry)

+ **Law of Large Numbers**

As the number of trials in a probability experiment increases, the difference in the theoretical probability of an event and the relative frequency approaches zero. The theoretical probability and relative frequency get closer together. (Aaron Hines)

+ **OR usually implies Addition**

If an outcome is in either one of or both sets of data present, then it is or. EX: A=[1,2,3] B={0,4,5] then A OR B =[0,1,2,3,4,5] (Pat Blaine)

+ **AND usually implies Multiplication**

If an outcome is in both sets of data then it is described as 'AND'. EX: A=[1,2,3] B=[3,4,5] then A AND B= [3] (Pat Blaine)

+ **Complementary Events**

A complementary event (A') consists of all the outcomes that did not accur in an event (A). So given that S=(1,2,3,4,5,6,7) and A=(1,3,5,7), A'=(2,4,6). (Joel Satterwhite)

+ **Conditional Probability**

** ** The conditional values is the probability of an event (A), given that (B) has already occurred. (Jared Mathews)

+ **Unusual Events**

An event is considered unusual if the probability of it happening or something more extreme is small. We usually take small to be less than 5% unless given otherwise. For example, finding 9 heads when flipping a coin 10 times would be an unusually high number of heads since the probability of getting 9 or more heads is very small, about a 1.1% chance. (Peter Parker)

## Discrete Random Variables

+ **Random Variable**

Something of interest in an experiment that is being studies. These variables are usually upper case Latin letters. (Tanner Heiman)

+ **Discrete**

+ **Probability Distribution Function**

+ **Expected Value**

The expected value is the assumed average someone will get after doing an experiment a large number of times. (Devin Sather)

+ **Mean of a Probability Distribution Function**

The long term average of multiple attempts of a statistical experiment (Kandan Evans)

+ **Standard Deviation of Probability Distribution Function**

+ **Useful Spreadsheet Formulas**

Given a relative frequency table

Mean = sumproduct(x-col, p-col)

STD = sqrt(sumproduct( (x-col - mean)^2, p-col ) )

+ **Binomial Formulas**

`P(x=a)={n!}/{a!(n-a)!}*p^a*q^(n-a)` =BINOMDIST(a,n,p,0)

`P(x<=a)=P(0)+P(1)+...+P(a)=\sum_{i=0}^a {n!}/{i!*(n-i)!}*p^i*q^(n-i)` =BINOMDIST(a,n,p,1)