Math252: Unit 4 - Probability

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Math252: Unit 4 - Probability

"Or"

Used to indicate the intersection of sets. Or = you add

"And"

Used to indicate the intersection of sets. And = you multiply

Possibility Tree

Example:

Definition: A visual representation of a probability experiment where each outcome corresponds to an "outcome." Furthermore, each branch shows the number of ways an outcome can occur.

Terminology

Mutually Exclusive Events (A & B): Two events, A and B, such that the occurance of an outcome in event A makes it impossible to occur in event B.

Event (E): A set E of some of the outcomes of an experient.

Sample Space (S): The set of all outcomes of an experiment.

Outcome: A result of one trial in an experiment.

Theoritical Probability

Equation: P(E) = n(E)/n(S) E = event S = equally likely outcomes n(E)/n(S) = denotes number of outcomes

Example: A teacher has 7 brown-eyed and 2 blue-eyed brunettes in her class, as well as 8 blue-eyed and 3 brown-eyed blondes. If a child is selected at random, a) What is the probability that the child is brown-eyed AND brunette? b) What is the probability the child is brown-eyed OR brunette?

Answer: a) 7/20 * There are 7 brown-eyed brunettes out of the 20 children mentioned. b) 10/20 or 1/2 * There are 7 brown-eyed brunettes and 3 brown-eyed blondes, so 7 + 3 = 10.

Definition: A determination of probability made by assuming the probability of each outcome. This is what *should* happen in a "perfect" world.

Independent Event(s)

Definition: When you have 2 events (A & B) where the probability of B isn't dependent on whether or not event A occurs.

Simulation

Definition: A method to determine answers to real problems by conducting experiments.

Links to Learn More

Link 3: Probability Calculator Website: (click hyperlink to right) ---> Comments: This website was a real interesting find to me but also a very great tool for those who struggle at first with Probability or are conducting large experiements. By inputting your experimental data into the calculator, it is able to find the exact number of outcomes for both single and multiple probability events. While it may not be the most helpful in *explaining* Probability, I do think it is a fun option that allows you to play around with different events.

Link 2: Khan Academy - Probability Website: (click hyperlink to right) ---> Comments: Khan Academy is a great tool for those who are visual and audio learners. It has multiple videos (over 20+) on Probability that go over examples and concepts. For those who are unaware, Khan Academy also hosts videos for a variety of other subjects as well, so overall it is a very good learning resource.

Link 1: Math Goodies - Probability Website: (click hyperlink to right) --> Comments: This is a great resource I found that discusses the basics of Probability. It is filled with helpful and easy to understand definitions and exampls, as well as interactive examples you can do on your own.

Law of Large Numbers

Definition: The experimental probability of an event approximates a fixed number more and more closely as the number of trials increases.

Experimental Probability

Example: Find how many ways you can draw a club or a face card from an ordinary deck of playing cards.

Answer: Face Cards - 3/ per suit x 4 suits = 12 face cards = 12/52 (probability you will draw a face) Clubs - 13 clubs = 13/52 = 1/4 (probability you will draw a club) Total: 12 + 13 = 25 = 25/52 (probability you will draw either a club or face

Equation: Pe(E) = r/n r = number of times specific event occured n = number of trials conducted

Definition: The ratio of the number of times a specific event occurs to the total number of trials conducted. This is what *actually* happens once the experiment is tested, as opposed to Theoretical where the conclusions are assumed.