Morin: Probability for the enthusiastic beginner

By David Morin

10 flashcards · Mathematics · by lakesare

  1. Event VS outcome?

    event = { a set of outcomes }, e.g .'drawing a heart' outcome, e.g. 'drawing King Hearts'

  2. [The 'and' probability] Formula for the joint probability? P(A and B) = ...

    Interestingly: There is actually no need for the "dependent" qualifier in the first line of this rule. P(B|A) stands for the probability that B occurs, given that A occurs. It is called a "conditional probability," because we are assuming a given condition, namely that A occurs.

  3. [The 'and' probability] What's the simplified formula of joint probability for independent events? P(A and B) = ...

  4. [The 'and' probability] What are the 2 ways to write down the joint probability formula? P(A and B) = ...

    There is nothing special about the order of A and B. We could just as well interchange the letters and write P(B and A) = P(B)·P(A|B). However, we know that P(B and A) = P(A and B), because it doesn’t matter which event you say first when you say that two events both occur.

  5. [The 'and' probability] Why is the P(A and B) for independent events is just a special case of the P(A and B) for dependent events?

    Because P(B|A) = P(B) if the events are independent!

  6. What do these statements imply about the events A and B?

    If either of these statements are true (and they are equivalent), then events A and B are independent.

  7. [The 'or' probability] What's the formula for the 'or' probability? P(A or B) = ...

  8. [The 'or' probability] What's the simplified formula for the 'or' probability for mutually exclusive events? P(A or B) = ...

    Two events are non-exclusive if it's possible for both events to happen.

  9. Two events can be mutually exclusive, and dependent. What is the relationship between these attributes?

    Just 'mutually exclusive => dependent'. Two events are either independent or dependent, and they are also either exclusive or nonexclusive. There are therefore 2 · 2 = 4 combinations of these characteristics.

  10. Give all 4 formulas. Probability both A and B events happen:P(A and B) Probability both A and B events happen, if they are independent:P(A and B) Probability either A or B events happen:P(A or B) Probability either A or B events happen, if they are mutually exclusive:P(A or B)

    Probability both A and B events happen:P(A and B) = P(A) * P(B | A) Probability both A and B events happen, if they are independent:P(A and B) = P(A) * P(B) Probability either A or B events happen:P(A or B) = P(A) + P(B) - P(A and B) Probability either A or B events happen, if they are mutually exclusive:P(A or B) = P(A) + P(B)