Probability theory
Probability: A numerical measure of the chance that an event will occur. Experiment: A process that generates well defined outcomes.
Sample space: The set of all experimental outcomes.
Sample point: An element of the sample space. A sample point represents an experimental outcome. Tree diagram: A graphical representation that helps in visualizing a multiple step experiment. Classical method: A method of assigning probabilities that is appropriate when all the experimental outcomes are equally likely. Relative frequency method: A method of assigning probabilities that is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the experiment is repeated large number of times. Subjective method: A method of assigning probabilities on judgment. Event: A collection of sample points.

Complement of A : The event consisting of all sample points that are not in A. Venn diagram: A graphical representation for showing symbolically the sample space and operations involving events in which the sample space is represented by a rectangle and events are represented as circles within the sample space. Union of A and B : The event consisting of all sample points belonging to A or B or both. Intersection of A and B : The event containing the sample points belonging to both A and B. Conditional probabilities: the probability of an event given that another event already occurred. Joint probability: The probability of two events both is occurring that is the probability of the intersection of two events. Marginal probabilities: The values in the margins of a joint probability table that provides the probabilities of each event separately. Independent events: Two events A and B where the events have no influence on each other. Priory probabilities: Initial estimates of the probabilities of events. Posterior probabilities: revised probabilities of events based on additional information. Bayes’ theorem: A...

...regular soda, and two types of bottles of water.
a. Suppose Evan chose a bottle from the refrigerator at random. Could we realistically say that the probability of choosing a diet soda is 7/3? Why or why not?
b. If there are 16 total bottles of diet soda, 8 total bottles of regular soda, and 4 total bottles of water, what is the probability of each of the following:
(i) Choosing a bottle of diet soda when a bottle is chosen at random
(ii) Choosing a...

...I. ProbabilityTheory
* A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
* The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical...

...Worksheet 5 (Chapter 3): Probability II
Name: ______________________________________________
Section: _________________________
For any of the following questions be sure to show appropriate work and give appropriate probability
statements.
1. Students taking the Graduate Management Admissions Test (GMAT) were asked about their
undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of
their responses follows....

...be able to ONEDefine probability. TWO Describe the classical, empirical, and subjective approaches to probability. THREEUnderstand the terms experiment, event, outcome, permutation, and combination. FOURDefine the terms conditional probability and joint probability. FIVE Calculate probabilities applying the rules of addition and multiplication. SIXUse a tree diagram to organize and compute probabilities....

...positions are filled at random form the 11 finalists, what is the probability of selecting:
A: 3 females and 2 males?
B: 4 females and 1 male?
C: 5 females?
D: At least 4 females?
Problem 2
By examining the past driving records of drivers in a certain city, an insurance company has determined the following (empirical) probabilities:
[pic]
If a driver in this city is selected at random, what is the probability that:
A: He or...

...t)
P (X > s + t)
P (X > t)
e−λ(s+t)
e−λt
e−λs
P (X > s)
– Example: Suppose that the amount of time one
spends in a bank is exponentially distributed with
mean 10 minutes, λ = 1/10. What is the probability that a customer will spend more than 15
minutes in the bank? What is the probability
that a customer will spend more than 15 minutes in the bank given that he is still in the bank
after 10 minutes?
Solution:
P (X > 15) = e−15λ = e−3/2 = 0.22
P (X...

...Karan negi
12.2
12.3 We use equation 2 to find out probability:
F(t)=1 – e^-Lt
1-e^-(0.4167)(10) = 0.98 almost certainty. This shows that probability of another arrival in the next 10 minutes.
Now we figure out how many customers actually arrive within those 10 minutes. If the mean is 0.4167, then
0.4167*10=4.2, and we can round that to 4.
X-axis represents minutes (0-10)
Y-axis represents number of people.
We can conclude from this chart that the...

...Probability and its Applications
Published in association with the Applied Probability Trust
Editors: S. Asmussen, J. Gani, P. Jagers, T.G. Kurtz
Probability and its Applications
Azencott et al.: Series of Irregular Observations. Forecasting and Model
Building. 1986
Bass: Diffusions and Elliptic Operators. 1997
Bass: Probabilistic Techniques in Analysis. 1995
Berglund/Gentz: Noise-Induced Phenomena in Slow-Fast Dynamical Systems:
A...