Probability Quiz
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Questions and Answers

What is the probability of getting an odd number from the set of outcomes?

  • 1.0
  • 0.25
  • 0.5 (correct)
  • 0.75

    • Which of the following numbers are considered favorable outcomes for obtaining an odd number?

  • 1, 2, 3
  • 1, 4, 5
  • 1, 3, 5 (correct)
  • 2, 4, 6

    • How many total outcomes are there in the scenario presented?

  • 6 (correct)
  • 3
  • 4
  • 5

    • If the favorable outcomes for getting an odd number are 1, 3, and 5, what is their ratio to the total outcomes?

    <p>3:6</p> Signup and view all the answers

    What does the expression P(odd) represent in the context of probability?

    <p>The probability of getting an odd number</p> Signup and view all the answers

    What is the number of favourable outcomes when determining the probability of getting a King or a Heart greater than 10?

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

    What is the probability of getting a King or a Heart greater than 10 expressed as a fraction?

    <p>$\frac{7}{52}$</p> Signup and view all the answers

    How does a probability tree diagram help in probability calculations?

    <p>It visually represents outcomes and their probabilities.</p> Signup and view all the answers

    What does the branching in a probability tree diagram indicate?

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

    What is one of the components that can be displayed on the branches of a probability tree diagram?

    <p>The probabilities of each outcome.</p> Signup and view all the answers

    What is the total number of possible outcomes when a family has three children?

    <p>8</p> Signup and view all the answers

    How many favourable outcomes result in more heads than tails when a family has three children?

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

    What is the probability of a family with three children having more heads than tails?

    <p>$\frac{1}{2}$</p> Signup and view all the answers

    Which of the following outcomes does NOT represent more heads than tails for three children?

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

    If the probability of getting more tails than heads is considered, what is its value?

    <p>0.25</p> Signup and view all the answers

    What is the total number of possible gender outcomes for a family of four with two children?

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

    Which of the following pairs represent the only combination of children with the same gender in a family of four?

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

    When tossing a fair die and a coin, how many total possible outcomes can be obtained?

    <p>8</p> Signup and view all the answers

    What is the probability of getting an even number when tossing a fair die?

    <p>$\frac{1}{2}$</p> Signup and view all the answers

    In the context of the dice and coin scenario, what is the probability of getting a head and an even number?

    <p>$\frac{1}{3}$</p> Signup and view all the answers

    What method can be used to visually represent the possible outcomes of two children in a family?

    <p>Tree diagram</p> Signup and view all the answers

    Which of the following statements is accurate regarding the gender outcomes for two children?

    <p>There are four unique ordered pairs possible if considering birth order.</p> Signup and view all the answers

    Which of the following represents an incorrect outcome for the gender combinations of two children?

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

    What is the total number of favorable outcomes when the first child is a boy or the second child is a girl?

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

    Which of the following outcomes represents the scenario where the first child is a boy?

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

    What is the probability that the first child is a boy or the second child is a girl?

    <p>0.75</p> Signup and view all the answers

    Which of the following correctly identifies the outcomes when the first child is a boy?

    <p>BBB, BGB, BGG</p> Signup and view all the answers

    If the first child is a boy, how many favorable outcomes exist for the second child being a girl?

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

    What are the outcomes for the scenario where the second child is a girl?

    <p>BGB, BGG, GGB, GGG</p> Signup and view all the answers

    Which option correctly sums both conditions: first child is a boy and second child is a girl?

    <p>3/4</p> Signup and view all the answers

    In the set of outcomes, how many total outcomes are possible for the birth of two children?

    <p>8</p> Signup and view all the answers

    What is the probability of getting at least 1 head and 1 tail when flipping a fair coin three times?

    <p>$\frac{3}{4}$</p> Signup and view all the answers

    Which event is excluded when calculating the probability of at least 1 head and 1 tail in three coin flips?

    <p>Getting only tails</p> Signup and view all the answers

    What form does the final expression for the probability take?

    <p>$1 - rac{2}{8}$</p> Signup and view all the answers

    What is the complement event being calculated in this context?

    <p>Getting only heads or only tails</p> Signup and view all the answers

    When calculating $P\left(\mathrm{\text{not at least 1 head and 1 tail}}\right)$, how many outcomes are considered?

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

    In the probability formula, what does the term $\frac{2}{8}$ represent?

    <p>Number of favorable outcomes for only heads or only tails</p> Signup and view all the answers

    What is the sample space for flipping a coin three times?

    <p>{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}</p> Signup and view all the answers

    If you were to calculate the probability of getting at least 2 heads in 3 flips, how would that differ from the current calculation?

    <p>It would require a different total outcome count</p> Signup and view all the answers

    Study Notes

    Probability and Counting

    • Probability is calculated as the ratio of favorable outcomes to the total possible outcomes.
    • Probability of an event (P(event)) ranges from 0 to 1 inclusively.
    • Probability 0 means an event will never occur.
    • Probability 1 means an event is certain to occur.

    Empirical Probability

    • Empirical probability is based on observed data from experiments.

    Theoretical Probability

    • Theoretical probability is derived from knowledge of the situation, not experimentation.

    Counting Methods

    • Curly brackets {} are used to enclose the outcomes of events.
    • Outcomes of tossing a die are {1, 2, 3, 4, 5, 6}.
    • Outcomes of flipping a coin are {H, T}.

    Probability Tree Diagrams

    • Probability tree diagrams help visualize and determine the possible outcomes of an experiment.
    • The process starts with a dot, creating branches for each outcome of the experiment.
    • The diagram shows the total number of possible outcomes.

    Fundamental Counting Principle

    • Calculate the total number of outcomes in independent events by multiplying the possibilities of each event.
    • This method is useful for situations with numerous outcomes that make listing all outcomes very difficult.

    Mutually Exclusive Events

    • Mutually exclusive events cannot occur simultaneously.
    • Addition law for mutually exclusive events simplifies to: P(event A or event B) = P(event A) + P(event B).

    Not Mutually Exclusive Events

    • Not mutually exclusive events can occur simultaneously.
    • General addition law for calculating the probability of either or both of two events is P(A or B) = P(A) + P(B) - P(A and B).

    Complementary Events

    • The probability of an event plus the probability of its complement equals 1.
    • Calculating the complement can sometimes be easier than directly calculating the event's probability.
    • Probability formula: P(event) = 1 - P(not event)

    Expected Value

    • Expected value is the long-run average value of an experiment if repeated many times.
    • It's calculated by multiplying each possible outcome's value by its probability, then summing these values.

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    GCNU311A Lecturer 2019 Probability PDF

    Description

    Test your knowledge on probability concepts and calculations with this interactive quiz. You will answer questions about favorable outcomes, total outcomes, and the use of probability tree diagrams. Perfect for students looking to reinforce their understanding of probability theory.

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