Quantitative Techniques COQT111 Unit 3 Quiz
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Questions and Answers

What is a marginal probability?

  • Probability of a single event occurring only (correct)
  • Probability of two events occurring together
  • Probability of multiple outcomes from separate events
  • Probability given that another event has occurred

    • Which type of probability represents the intersection of two events?

  • Marginal probability
  • Independent probability
  • Joint probability (correct)
  • Conditional probability

    • How is conditional probability represented mathematically?

  • P(A ∩ B)
  • P(A + B)
  • P(A|B) (correct)
  • P(A - B)

    • What type of table is typically used to find joint probabilities?

    <p>Cross tabulation</p> Signup and view all the answers

    In the example given, what is the probability of being female and belonging to blood group O?

    <p>0.19</p> Signup and view all the answers

    Which statement correctly defines joint probability?

    <p>It represents the probability that two events occur together.</p> Signup and view all the answers

    Why is marginal probability called 'marginal'?

    <p>It uses values from the margins of a frequency table.</p> Signup and view all the answers

    What does conditional probability require?

    <p>The occurrence of event B before event A</p> Signup and view all the answers

    What is the range of probability values for any event?

    <p>0 to 1</p> Signup and view all the answers

    What does a probability of 0 signify?

    <p>An event is impossible to occur</p> Signup and view all the answers

    What is the sum of probabilities of all possible events in a sample space?

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

    If the probability of event A occurring is 0.6, what is the probability of it not occurring?

    <p>0.4</p> Signup and view all the answers

    Which of the following is a property of mutually exclusive events?

    <p>They cannot occur at the same time</p> Signup and view all the answers

    What is complementary probability?

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

    Which of the following defines

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

    What does it mean for events to be collectively exhaustive?

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

    What is the value of $5!$?

    <p>120</p> Signup and view all the answers

    How many distinct arrangements can be made with 5 speakers?

    <p>120</p> Signup and view all the answers

    In selecting a captain and vice-captain from 5 speakers, how many different pairs can be formed?

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

    Which formula represents the number of permutations of selecting $r$ objects from $n$ objects?

    <p>$\frac{n!}{(n-r)!}$</p> Signup and view all the answers

    What distinguishes a permutation from a combination?

    <p>Order matters in permutations but not in combinations.</p> Signup and view all the answers

    What is the formula for calculating combinations?

    <p>$\frac{n!}{r!(n-r)!}$</p> Signup and view all the answers

    If a process has 3 outcomes for event 1 and 4 outcomes for event 2, what is the total number of outcomes?

    <p>12</p> Signup and view all the answers

    How many ways can you choose 2 objects from a set of 5 when the order does not matter?

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

    What is the probability of selecting a female from the population?

    <p>0.5</p> Signup and view all the answers

    What is the probability that an individual has blood group AB?

    <p>0.157</p> Signup and view all the answers

    If events A (Female) and B (Blood group AB) are not mutually exclusive, what is the formula used to find the probability of either event occurring?

    <p>P(A ∪ B) = P(A) + P(B) - P(A ∩ B)</p> Signup and view all the answers

    What would the probability be if events A (Blood group O) and B (Blood group AB) are mutually exclusive?

    <p>0.5140</p> Signup and view all the answers

    If the joint probability of events A and B is desired for dependent events, which rule should be applied?

    <p>Multiplication rule</p> Signup and view all the answers

    What is the correct interpretation of mutually exclusive events?

    <p>They cannot occur together in a single trial.</p> Signup and view all the answers

    What is the intersection probability for events A (Female) and B (Blood group AB)?

    <p>0.0714</p> Signup and view all the answers

    Which of the following statements is TRUE regarding the probability of selecting a person with blood group AB or a female?

    <p>P(A ∪ B) = 0.5856</p> Signup and view all the answers

    How many ways can a basketball team of 5 players be chosen from 9 players?

    <p>126</p> Signup and view all the answers

    What defines a discrete random variable?

    <p>It can take on a finite or countably infinite number of distinct possible values.</p> Signup and view all the answers

    Which of the following is an example of a discrete probability distribution?

    <p>Number of faulty machines at a company</p> Signup and view all the answers

    What is a characteristic of continuous probability distributions?

    <p>They take on an infinite number of possible values.</p> Signup and view all the answers

    What is a probability distribution?

    <p>A list of all possible outcomes and their probabilities.</p> Signup and view all the answers

    Which type of probability distribution is classified as continuous?

    <p>Normal distribution</p> Signup and view all the answers

    Which of the following represents a discrete random variable?

    <p>The number of enrolled Engineering students</p> Signup and view all the answers

    Which of the following statements is true regarding discrete probability distributions?

    <p>Each outcome has a non-zero probability.</p> Signup and view all the answers

    What is the characteristics of occurrences in a Poisson process?

    <p>They occur uniformly distributed over time.</p> Signup and view all the answers

    Which of the following examples is NOT typically modeled as a Poisson process?

    <p>The total sales of a store on a holiday.</p> Signup and view all the answers

    What does the symbol λ represent in the Poisson probability distribution formula?

    <p>The mean number of occurrences of the outcome.</p> Signup and view all the answers

    In the Poisson probability distribution, what is the probability of observing 0 occurrences when λ = 1.9?

    <p>$P(X = 0) = e^{-1.9} \cdot 1.9^0 / 0!$</p> Signup and view all the answers

    Which statement is true about the occurrences in a Poisson process?

    <p>Occurrences can take any integer value from 0 to infinity.</p> Signup and view all the answers

    What type of distribution does the number of typographical errors in a dissertation follow?

    <p>Poisson Distribution</p> Signup and view all the answers

    If λ of a Poisson process is increased, what happens to the probability of observing fewer events?

    <p>It decreases.</p> Signup and view all the answers

    For the Poisson formula, what does 'e' approximately equal to?

    <p>2.71828</p> Signup and view all the answers

    Study Notes

    Quantitative Techniques (COQT111) Unit 3: Foundation of Statistical Inference

    • This unit covers the foundations of statistical inference, focusing on probability
    • The unit overview discusses estimating proportions of customers favoring a product via surveys, highlighting the inherent uncertainty in survey results and the importance of calculating likelihoods in management decisions
    • Learning outcomes emphasize calculating probabilities using contingency tables, Poisson and Binomial formulas, including cumulative probabilities

    1. Basic Probability Concepts

    • Probability is the likelihood of an event occurring
    • An experiment is a process that yields an outcome
    • Outcomes are results of an experiment
    • An event is a specific outcome or group of outcomes
    • The sample space is the set of all possible outcomes
    • Probability is expressed as a ratio (number of favorable outcomes/total possible outcomes)
    • Probability values range from 0 (impossible) to 1 (certain)

    1.1 Types of Probability

    • Subjective probability relies on personal feelings or insights
    • Objective probability uses scientific methods like surveys to determine probabilities

    1.2 Properties of Probability

    • Probability values always lie between 0 and 1 (inclusive)
    • If an event is impossible, its probability is 0
    • If an event is certain, its probability is 1
    • The sum of probabilities of all possible outcomes equals 1
    • Complementary probability: The probability of an event not occurring equals 1 minus the probability of the event occurring

    1.3 Probability Concepts

    • Intersection: The intersection of events A and B (A ∩ B) includes elements in both A and B
    • Union: The union of events A and B (A ∪ B) includes elements in either A, B, or both
    • Mutually Exclusive: Events that cannot occur together
    • Collectively Exhaustive: Events whose union is the entire sample space

    2. Probability Distributions

    • Probability distributions list all possible outcomes and their probabilities
    • Discrete distributions have countable outcomes (e.g., binomial, Poisson)
    • Continuous distributions have uncountable outcomes (e.g., normal)

    2.1 Types of Probability Distributions

    • Discrete distributions: Binomial, Poisson
    • Continuous distribution: Normal

    2.2 Discrete Probability Distributions

    • Examples: number of enrolled students; faulty machines
    • Each outcome in a discrete distribution has a non-zero probability

    2.3 Binomial Probability Distribution

    • Conditions: n trials; two outcomes (success/failure); constant probability of success

    2.4 Poisson Probability Distribution

    • Conditions: fixed time/space/volume; independent events; constant average rate of events

    3. Unit Summary

    • Summarizes unit content, providing a comprehensive overview of probability concepts, probability distributions, and sampling methods

    4. References

    • Lists sources utilized for the unit information

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    Unit 3 - Quantitative Techniques (COQT111) PDF

    Description

    Test your knowledge on the foundations of statistical inference, focusing on probability and its applications in estimating customer preferences. This quiz covers basic probability concepts, including events, outcomes, and sample spaces, along with calculating likelihoods. Prepare to enhance your understanding of how these concepts are vital for informed management decisions.

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