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Multiplication Rule: Independent Events quiz

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  • What does it mean for two events to be independent?
    Two events are independent if the outcome of one does not affect the outcome of the other.
  • How do you calculate the probability of two independent events both occurring?
    Multiply the probability of the first event by the probability of the second event.
  • What is the probability of getting heads on two consecutive coin flips?
    The probability is (1/2) × (1/2) = 1/4 or 0.25.
  • What is 'and probability' in the context of independent events?
    'And probability' refers to the probability that both events occur, calculated by multiplying their individual probabilities.
  • How can you tell if two events are dependent?
    Two events are dependent if the outcome of one affects the probability of the other.
  • What is the probability of rolling an even number and then a three on a six-sided die?
    The probability is (3/6) × (1/6) = 3/36 or 0.08.
  • If you draw and keep a blue marble, then draw again, are these events independent?
    No, because removing a marble changes the probability for the second draw, making the events dependent.
  • What symbol is often used in set notation to represent 'and' probability?
    The upside down 'U' symbol (∩) is used to represent 'and' probability.
  • How do you find the probability of three independent events all occurring?
    Multiply the probabilities of all three events together.
  • Why is the probability of getting heads on two coin flips 1/4?
    Because there are four possible outcomes and only one is heads on both flips.
  • What is the probability of rolling a three on a six-sided die?
    The probability is 1/6.
  • If the outcome of one event does not change the probability of another, what are the events called?
    They are called independent events.
  • What do you do if you need to find the 'and probability' for more than two independent events?
    Continue multiplying the probability of each event together.
  • Give an example of two independent events.
    Flipping a coin and rolling a die are independent because one does not affect the other.
  • What is the probability of getting tails on the first coin flip and heads on the second?
    The probability is (1/2) × (1/2) = 1/4.