Probability and Statistics Lecture 1
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Questions and Answers

What is the definition of probability?

  • A measure of certainty
  • The frequency of an event
  • The number of possible outcomes
  • A measure of uncertainty (correct)

    • What is a sample space?

  • The set of all possible outcomes of an experiment (correct)
  • The probability of an event
  • A single outcome of an experiment
  • A subset of all possible outcomes

    • What is an event in probability?

  • A subset of a sample space (correct)
  • A single outcome of an experiment
  • The probability of an event
  • The set of all possible outcomes

    • What is a simple event?

    <p>An event containing only one outcome</p> Signup and view all the answers

    What is a compound event?

    <p>An event containing more than one outcome</p> Signup and view all the answers

    What is the complement of an event?

    <p>The event not occurring</p> Signup and view all the answers

    What are mutually exclusive events?

    <p>Events that cannot occur together</p> Signup and view all the answers

    What is the total number of people in the group?

    <p>200</p> Signup and view all the answers

    In the experiment of rolling a die, what is the event 'A or B'?

    <p>The event of getting a prime number or an odd number</p> Signup and view all the answers

    How many people have type AB blood?

    <p>15</p> Signup and view all the answers

    What is the probability that a person selected at random has O blood type?

    <p>7/20</p> Signup and view all the answers

    How many students like Mathematics in the survey?

    <p>40</p> Signup and view all the answers

    How many students like both Mathematics and English?

    <p>10</p> Signup and view all the answers

    How many students like all three subjects in the survey?

    <p>5</p> Signup and view all the answers

    What is a Venn diagram used to represent?

    <p>Differences and similarities between two concepts</p> Signup and view all the answers

    What does P(E) or Pr(E) denote?

    <p>Probability of event E</p> Signup and view all the answers

    What is the formula for determining probability using the classical method?

    <p>P(E) = number of outcomes in the event / total number of outcomes</p> Signup and view all the answers

    What are two events that do not depend on each other?

    <p>Independent events</p> Signup and view all the answers

    What is the rule that states P(S) = 1?

    <p>Axiom 2</p> Signup and view all the answers

    What is the probability of an event that is certain to occur?

    <p>1</p> Signup and view all the answers

    What is the probability of rolling an even number on a die?

    <p>1/2</p> Signup and view all the answers

    What is the probability of obtaining two heads when two coins are tossed?

    <p>1/4</p> Signup and view all the answers

    Study Notes

    Probability

    • Probability is a measure of uncertainty
    • Sample Space: Set of all possible outcomes of an experiment

    Events

    • An event is a subset of a sample space of some experiment
    • Simple Event: An event containing only one outcome
    • Compound Event: An event containing more than one outcome

    Event Operations

    • Complement
    • Intersection
    • Mutually Exclusive Events: If event A and B cannot occur together
    • Union

    Venn Diagrams

    • Used to visually represent the differences and similarities between two concepts
    • Typically uses intersecting and non-intersecting circles

    Axioms of Probability

    • Axiom 1: For any event, P(A) ≥ 0
    • Axiom 2: P(S) = 1, where S is the sample space

    Determining Probability

    • Classical Method: P(E) = Number of outcomes in the event / Total number of outcomes in the sample space

    Independent Events

    • Let's say we have two events A and B
    • If the occurrence of A does not depend on the occurrence of B

    Rules of Probability

    • Complement Rule
    • Addition and Multiplication Rule

    Probability Problems

    • Rolling a die: Find the probability that an even number is obtained
    • Two coins are tossed: Find the probability that two heads are obtained
    • Person selected at random: Find the probability that this person has O blood type
    • Survey of students: Find the probability that a student selected likes Mathematics or Science, etc.

    Exercise

    • Students like Mathematics, Science, and English: Find the probability of various events

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    Description

    This quiz covers the basics of probability, Venn diagrams, and statistics, as part of the CS 1212 and IT 1213 course. Test your understanding of these fundamental concepts in computer science and IT.

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