Determine whether the following pair of events are dependent or independent.
Event E is the event that a resident of Pennsylvania lives in Pittsburgh, and F is the event that a resident of Pennsylvania lives in either Pittsburgh or Philadelphia.
Solution:-
Two events, E and F, are dependent if the outcome of event E influences the outcome of event F, and vice versa. Event E and F are independent if the outcome of E does not affect the outcome of event F, and vice versa.
Notice that the fact that a resident of Pennsylvania lives in Pittsburgh influences the fact that a resident of Pennsylvania lives in either Pittsburgh or Philadelphia, because if a resident of Pennsylvania lives in Pittsburgh, it is certain that the resident of Pennsylvania lives in Pittsburgh or Philadelphia.
Therefore, the two events are dependent.