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Basic Concepts of Probability quiz #1

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  • What is the difference between theoretical probability and empirical probability?
    Theoretical probability is calculated based on possible outcomes before any events occur, while empirical probability is based on actual observed outcomes from experiments or data.
  • How do you calculate the theoretical probability of an event?
    Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
  • How is empirical probability determined?
    Empirical probability is determined by dividing the number of times an event actually occurs by the total number of trials conducted.
  • What is the sample space in probability, and how is it represented?
    The sample space is the set of all possible outcomes of an experiment, represented using set notation with curly brackets.
  • If you flip a fair coin, what is the theoretical probability of getting heads?
    The theoretical probability of getting heads when flipping a fair coin is 1/2.
  • If you roll a six-sided die, what is the theoretical probability of rolling a number greater than three?
    The theoretical probability of rolling a number greater than three on a six-sided die is 3/6, which simplifies to 1/2 or 0.5.
  • If you roll a six-sided die 10 times and get a number greater than three in 8 of those rolls, what is the empirical probability of this event?
    The empirical probability is 8/10, which simplifies to 0.8.
  • Why might empirical probability differ from theoretical probability in a small number of trials?
    Empirical probability may differ from theoretical probability in a small number of trials due to random variation and a limited sample size.
  • How does increasing the number of trials in an experiment affect empirical probability?
    Increasing the number of trials generally causes the empirical probability to get closer to the theoretical probability.
  • What notation is commonly used to represent the probability of an event, and how would you write the probability of rain?
    Probability is commonly represented as P(event), so the probability of rain would be written as P(rain).