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Addition Rule quiz

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  • What does it mean for two events to be mutually exclusive?
    Mutually exclusive events cannot occur at the same time; if one happens, the other cannot.
  • How do you calculate the probability of two mutually exclusive events occurring?
    Add the individual probabilities of each event: P(A or B) = P(A) + P(B).
  • What is the formula for the probability of two non-mutually exclusive events?
    P(A or B) = P(A) + P(B) - P(A and B).
  • Why do you subtract P(A and B) when calculating the probability of non-mutually exclusive events?
    Because the overlap (where both events occur) is counted twice when adding P(A) and P(B), so it must be subtracted once.
  • What does the symbol '∪' represent in probability notation?
    The symbol '∪' means 'or' and represents the union of two events.
  • What does the symbol '∩' represent in probability notation?
    The symbol '∩' means 'and' and represents the intersection where both events occur.
  • If two events are mutually exclusive, what is P(A and B)?
    P(A and B) is 0 because both events cannot happen at the same time.
  • Give an example of two mutually exclusive events.
    Getting heads or tails on a single coin flip; you cannot get both at once.
  • Give an example of two non-mutually exclusive events.
    Rolling a six and rolling a number higher than three on a die; rolling a six satisfies both events.
  • How would you calculate the probability of rolling a 3 or a 5 on a six-sided die?
    Add the probabilities: 1/6 (for 3) + 1/6 (for 5) = 2/6 or 1/3.
  • How do you find the probability of rolling a number greater than 3 or an even number on a six-sided die?
    Add the probabilities of each event, then subtract the overlap: 3/6 + 3/6 - 2/6 = 4/6 or 2/3.
  • What is the general addition rule for any two events?
    P(A or B) = P(A) + P(B) - P(A and B), regardless of mutual exclusivity.
  • When can you use the simple addition rule without subtracting the overlap?
    When the events are mutually exclusive, since P(A and B) = 0.
  • What is 'or probability' in the context of probability rules?
    'Or probability' refers to the probability that at least one of two events occurs.
  • Why is understanding mutually exclusive and non-mutually exclusive events important in probability?
    It ensures you use the correct formula and avoid double-counting outcomes when calculating probabilities.