Mutltiplication Rule
Dependent Events

When the outcome or occurrence of the first event affects the outcome or occurrence of the second event in such a way that the probability is changed, the events are said to be dependent events.

Example(s):

Drawing a card from a deck, not replacing it, and then drawing a second card
Selecting a ball from an urn, not replacing it, and then selecting a second ball
Being a lifeguard and getting a suntan
Having high grades and getting a scholarship

When two events are dependent we have another multiplication rule:

\[P(A\text{ and }B)=P(A)\cdot P(B|A)\]

Mutltiplication RuleDependent Events

Mutltiplication Rule
Dependent Events