Probability Concepts and Formulas Quiz
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Questions and Answers

What is the probability that X is equal to 2 in the example provided?

  • 3/8 (correct)
  • 1/8
  • 1/3
  • 1/4

    • If P(X) must be between 0 and 1, which of the following ranges is invalid?

  • (0, 1)
  • (0.5, 1)
  • (0, 0.5) (correct)
  • (0.2, 1)

    • In a probability histogram, what does the vertical axis represent?

  • Total number of possible outcomes
  • Number of times an event occurred
  • Values of a random variable
  • Probability of an event (correct)

    • If the sum of all possible probabilities is 1, what does this imply?

    <p>At least one event is certain to happen</p> Signup and view all the answers

    Given a random variable X that represents the number of heads in three coin tosses, what is P(X=1)?

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

    What happens if the probability of an event is zero according to the text?

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

    What does the mean represent in the context of a discrete random variable?

    <p>The expected value, obtained by the weighted average of all possible values</p> Signup and view all the answers

    What does the variance of a discrete random variable measure?

    <p>The spread or dispersion of the random variable's values</p> Signup and view all the answers

    Which formula is used to calculate the variance of a discrete random variable?

    <p>$σ^2 = ∑ (x - μ)^2 P(x)$</p> Signup and view all the answers

    What does the standard deviation of a discrete random variable measure?

    <p>The spread or dispersion relative to the mean</p> Signup and view all the answers

    In a probability distribution, if P(x) = 4/25, what does this value represent?

    <p>Probability of the random variable x occurring</p> Signup and view all the answers

    What is the purpose of calculating the mean in probability distributions?

    <p>To find the expected value of the random variable</p> Signup and view all the answers

    What is the probability of rolling a number less than 5 on a six-sided die?

    <p>2/3</p> Signup and view all the answers

    If you randomly select a letter from the word 'PROBABILITY', what is the probability of selecting a vowel?

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

    When a fair six-sided die is rolled, what is the probability of rolling a prime number?

    <p>1/3</p> Signup and view all the answers

    If you spin a spinner with 8 equal sections numbered 1 through 8, what is the probability of landing on a multiple of 4?

    <p>1/8</p> Signup and view all the answers

    When drawing a card from a standard deck, what is the probability of drawing a black card?

    <p>26/52</p> Signup and view all the answers

    A jar contains 8 red marbles and 5 blue marbles. What is the probability of randomly selecting a red marble?

    <p>$5/8$</p> Signup and view all the answers

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