Multiplication rule for "AND" - Probability

Multiplication rule for "AND"

Lessons

Notes:
\cdot P(A and B): probability of event A occurring and then event B occurring in successive trials.

\cdot P(B | A): probability of event B occurring, given that event A has already occurred.

\cdot P(A and B) = P(A) \cdot P(B | A)

\cdot Independent Events
If the events A, B are independent, then the knowledge that event A has occurred has no effect on the probably of the event B occurring, that is P(B | A) = P(B).
As a result, for independent events: P(A and B) = P(A) \cdot P(B | A)
= P(A) \cdot P(B)
  • 3.
    Independent Events VS. Dependent Events
  • 4.
    Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls.
    A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A;
    if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.
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Multiplication rule for "AND"

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