{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CS2800-Probability_part_a_v.1

CS2800-Probability_part_a_v.1 - Discrete Math CS 280 Prof...

Info icon This preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Discrete Math CS 280 Prof. Bart Selman [email protected] Module Probability --- Part a) Introduction
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 Terminology Experiment A repeatable procedure that yields one of a given set of outcomes Rolling a die, for example Sample space The set of possible outcomes For a die, that would be values 1 to 6 Event A subset of the sample experiment If you rolled a 4 on the die, the event is the 4
Image of page 2
Probability Experiment : We roll a single die, what are the possible outcomes? {1,2,3,4,5,6} The set of possible outcomes is called the sample space. Depends on what we’re going to ask. Often convenient to choose a sample space of equally likely outcomes. {(1,1),(1,2),(1,3),…,(2,1),…,(6,6)} We roll a pair of dice, what is the sample space?
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 Probability definition: Equally Likely Outcomes The probability of an event occurring (assuming equally likely outcomes) is: Where E an event corresponds to a subset of outcomes. Note: E S. Where S is a finite sample space of equally likely outcomes Note that 0 ≤ |E| ≤ |S| Thus, the probability will always between 0 and 1 An event that will never happen has probability 0 An event that will always happen has probability 1 S E E p = ) (
Image of page 4
5 Probability is always a value between 0 and 1 Something with a probability of 0 will never occur Something with a probability of 1 will always occur You cannot have a probability outside this range! Note that when somebody says it has a “100% probability” That means it has a probability of 1
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Dice probability What is the probability of getting a 7 by rolling two dice? There are six combinations that can yield 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) Thus, |E| = 6, |S| = 36, P(E) = 6/36 = 1/6
Image of page 6
Probability Which is more likely: Rolling an 8 when 2 dice are rolled? Rolling an 8 when 3 dice are rolled? No clue.
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Probability What is the probability of a total of 8 when 2 dice are rolled? What is the size of the sample space? 36 How many rolls satisfy our property of interest? 5 So the probability is 5/36 ≈ 0.139.
Image of page 8
Probability What is the probability of a total of 8 when 3 dice are rolled? What is the size of the sample space? 216 How many rolls satisfy our condition of interest? C(7,2) So the probability is 21/216 ≈ 0.097.
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
10 The game of poker You are given 5 cards (this is 5-card stud poker) The goal is to obtain the best hand you can The possible poker hands are (in increasing order): No pair One pair (two cards of the same face) Two pair (two sets of two cards of the same face) Three of a kind (three cards of the same face) Straight (all five cards sequentially – ace is either high or low) Flush (all five cards of the same suit) Full house (a three of a kind of one face and a pair of another face) Four of a kind (four cards of the same face) Straight flush (both a straight and a flush) Royal flush (a straight flush that is 10, J, K, Q, A)
Image of page 10
11 Poker probability: royal flush What is the chance of getting a royal flush?
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern