Conditional Probability and Tree Diagrams
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Questions and Answers

What is the probability of each outcome in the given table?

  • 1 in 12
  • 1 in 6
  • 1 in 3
  • 1 in 9 (correct)
  • What is the operation used to construct the table of outcomes?

  • Addition of their values
  • Division of their values
  • Subtraction of their values
  • Multiplication of their values (correct)
  • What are Event 1 and Event 2 in the given example?

  • Dice roll 1-4 and Dice roll 1-4
  • Dice roll 1-3 and Dice roll 1-3
  • Dice roll 1-6 and Dice roll 1-6 (correct)
  • Dice roll 1-5 and Dice roll 1-5
  • What is the purpose of constructing the table of outcomes?

    <p>To calculate the combined outcomes</p> Signup and view all the answers

    What is the combined outcome when Event X has outcome B and Event Y has outcome 3?

    <p>B3</p> Signup and view all the answers

    What is the number of possible outcomes in the given table?

    <p>9^2</p> Signup and view all the answers

    What is the purpose of a table of outcomes?

    <p>To show the possible results of two independent events</p> Signup and view all the answers

    When are events considered independent?

    <p>When the probability of one event does not affect the probability of the other</p> Signup and view all the answers

    How are the outcomes of two events displayed in a table of outcomes?

    <p>One event is displayed vertically, and the other horizontally</p> Signup and view all the answers

    What does each box in a table of outcomes represent?

    <p>One possible combined outcome</p> Signup and view all the answers

    What is the advantage of using a table of outcomes?

    <p>It makes it easier to calculate the probability of each possible outcome</p> Signup and view all the answers

    What do the rows and columns in a table of outcomes represent?

    <p>The outcomes of one event and the outcomes of the other event</p> Signup and view all the answers

    What is the probability of a particular outcome in a given event?

    <p>The number of target outcomes divided by the total number of outcomes</p> Signup and view all the answers

    What is the first step in calculating the probability of a combined outcome?

    <p>Identify the target outcome and count the number of appearances</p> Signup and view all the answers

    What is the purpose of constructing a table of outcomes?

    <p>To calculate the probability of each combined outcome</p> Signup and view all the answers

    What is the formula for calculating the probability of a particular outcome?

    <p>P = T / n</p> Signup and view all the answers

    What is the condition for calculating the probability of a combined outcome?

    <p>The outcomes must be independent</p> Signup and view all the answers

    What is the concept of calculating the probability of a particular outcome based on a condition?

    <p>Conditional Probability</p> Signup and view all the answers

    What is the outcome of rolling two fair, six-sided dice at the same time?

    <p>A product that may or may not be a square number</p> Signup and view all the answers

    What is the purpose of the example problem about rolling two fair, six-sided dice?

    <p>To illustrate the concept of conditional probability</p> Signup and view all the answers

    Study Notes

    Tables of Outcomes

    • A table of outcomes is a visual method of showing the possible results of two independent events.
    • The table can be used to find the probability of each possible outcome occurring.
    • Events are independent if the probability of one event occurring does not affect the probability of the other event occurring.

    Constructing a Table of Outcomes

    • One event's outcomes are displayed vertically, and the other's displayed horizontally.
    • Each box in the table represents one possible combined outcome.
    • The table can be used to calculate the probability of each combined outcome.

    Calculating Probability

    • The probability of a particular outcome is the number of target outcomes divided by the total number of outcomes.
    • The formula to calculate probability is: P = (Number of target outcomes) / (Total number of outcomes)

    Example: Rolling Two Dice

    • Two fair, six-sided dice are rolled at the same time.
    • The table of outcomes shows the possible results of rolling the two dice.
    • The probability of each combined outcome can be calculated using the table.

    Example: Calculating Probability of a Square Number

    • Two fair, six-sided dice are rolled at the same time.
    • The probability of their product being a square number can be calculated using the table of outcomes.
    • The table of outcomes can be used to identify the target outcomes and calculate the probability.

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    Description

    This quiz assesses understanding of conditional probability and tree diagrams, focusing on combined outcomes of events. Test your skills in probability theory!

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