Probability Theory: Sample Space and Events
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Questions and Answers

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

  • more than 1
  • 0
  • 1/2
  • 1 (correct)

    • What is the probability of an event that is impossible to happen?

  • 1
  • less than 0
  • 1/2
  • 0 (correct)

    • What is the probability of getting a head when a coin is tossed?

  • 1/2 (correct)
  • 1/3
  • 3/4
  • 2/3

    • What is the probability of any one outcome when a single die is thrown?

    <p>1/6</p> Signup and view all the answers

    What is the condition for the classical definition of probability to be applicable?

    <p>The cases are exhaustive, mutually exclusive and equally likely</p> Signup and view all the answers

    What is the purpose of a probability line?

    <p>To represent the probability of events on a linear axis</p> Signup and view all the answers

    What is the meaning of probability in simple terms?

    <p>How likely something is to happen</p> Signup and view all the answers

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

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

    Who is credited with the creation of probability theory?

    <p>Blaise Pascal and Pierre de Fermat</p> Signup and view all the answers

    What was the problem that Chevalier de Méré presented to Pascal?

    <p>To decide whether to place a bet on the occurrence of at least a 'double six' out of the 24 throws</p> Signup and view all the answers

    What is the objective of applying probability in data treatment?

    <p>To make informed decisions based on data</p> Signup and view all the answers

    What is the concept of conditional probability related to?

    <p>Probability of an event occurring given another event has occurred</p> Signup and view all the answers

    What is probability?

    <p>A guide to what might happen</p> Signup and view all the answers

    What is the Sample Space composed of?

    <p>All possible outcomes</p> Signup and view all the answers

    What is an Event in probability?

    <p>One or more outcomes</p> Signup and view all the answers

    What is the purpose of understanding probability?

    <p>To get a feel for random events</p> Signup and view all the answers

    What is the term for the individual outcomes in the Sample Space?

    <p>Sample Points</p> Signup and view all the answers

    How many Sample Points are in the Sample Space when throwing 2 dice?

    <p>36</p> Signup and view all the answers

    What is an example of an event that includes several outcomes?

    <p>Choosing a King from a deck of cards</p> Signup and view all the answers

    What type of events are affected by previous events?

    <p>Dependent Events</p> Signup and view all the answers

    What is the purpose of a tree diagram in probability?

    <p>To help with dependent events</p> Signup and view all the answers

    What is the characteristic of mutually exclusive events?

    <p>They can't happen at the same time</p> Signup and view all the answers

    What is the probability of Coach Sam being the coach in a soccer game?

    <p>0.6</p> Signup and view all the answers

    What type of event is rolling a 5 on a dice?

    <p>Single Outcome Event</p> Signup and view all the answers

    What is an event in a random experiment?

    <p>A subset of the sample space of the experiment</p> Signup and view all the answers

    What is the sample space of the experiment of measuring the lifetime of a lightbulb?

    <p>[0, ∞)</p> Signup and view all the answers

    What is the purpose of conditional probability?

    <p>To calculate the probability of an event occurring based on the occurrence of a previous event</p> Signup and view all the answers

    What is the sample space of the experiment of choosing a point from the interval (0, 1)?

    <p>(0, 1)</p> Signup and view all the answers

    What is the event in the experiment of tossing a coin until one gets a Heads?

    <p>{H, T H, T T H, T T T H,...}</p> Signup and view all the answers

    How is conditional probability calculated?

    <p>By multiplying the probability of the preceding event by the updated probability of the succeeding event</p> Signup and view all the answers

    Study Notes

    Classical Definition of Probability

    • The probability of an event A is defined as the number of favorable outcomes (m) divided by the total number of equally likely outcomes (n).
    • Example: Coin toss - probability of getting a head is 1/2 (1 favorable outcome out of 2 equally likely outcomes).
    • Example: Single die throw - probability of any one outcome is 1/6 (1 favorable outcome out of 6 equally likely outcomes).

    Probability Line

    • A representation of probability on a linear axis, where the probability of an event ranges from 0 (impossible) to 1 (certain).
    • The probability of an event will not be less than 0, as it is impossible for something to not happen.
    • The probability of an event will not be more than 1, as it is certain that something will happen.

    Introduction to Probability

    • Probability implies 'likelihood' or 'chance'.
    • It is a measure of how likely something is to happen.
    • When an event is certain to happen, the probability of occurrence is 1, and when it is certain that the event cannot happen, the probability is 0.

    Roots of Probability

    • The concept of probability was created by French mathematicians Blaise Pascal and Pierre de Fermat in 1654.
    • They were approached by Chevalier de Méré, a French nobleman, to resolve an apparent contradiction in a dice game.
    • The game involved throwing a pair of dice 24 times, with the goal of determining the probability of getting at least one "double six".

    Probability as a Guide

    • Probability does not predict exactly what will happen, but rather serves as a guide.
    • It provides a measure of the likelihood of an event occurring.

    Sample Space and Events

    • The sample space is the set of all possible outcomes of an experiment.
    • An event is a subset of the sample space.
    • Example: Throwing two dice - the sample space is all possible outcomes (36 sample points), and the event of getting a "double" is a subset of 6 sample points.

    Types of Events

    • Events can be independent (not affected by other events), dependent (affected by other events), or mutually exclusive (cannot happen at the same time).
    • Examples: Tossing a coin, rolling a dice, drawing a lottery ticket.

    Conditional Probability and Independence

    • Conditional probability is the likelihood of an event occurring based on the occurrence of a previous event.
    • It is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding event.
    • Example: A soccer game where the probability of being the goalkeeper depends on the coach.

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    Description

    Test your understanding of sample space and events in probability theory with this quiz. Learn how to identify and define events in different scenarios, including tossing coins, measuring lifetime, and more. Improve your skills in probability theory and statistics.

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