June 2020
Intermediate to advanced
382 pages
11h 39m
English
Content preview from 40 Algorithms Every Programmer Should Know
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The general multiplication rule
If two or more events are dependent, the general multiplication rule is used. This formula is actually valid in both cases of independent and dependent events:
P(outcome 1 AND outcome 2)=P(outcome 1)*P(outcome 2 | outcome 1)
Note that P(outcome 2 | outcome 1) refers to the conditional probability of outcome 2 occurring given outcome 1 has already occurred. The formula incorporates the dependence between the events. If the events are independent, then the conditional probability is irrelevant as one outcome does not influence the chance of the other occurring, and P(outcome 2 | outcome 1) is simply P(outcome 2). Note that the formula in this case just becomes the simple multiplication rule.