Conditional Probability and Independence: Basics 1

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Page 1 - Conditional Probability: Dependence and Independence

The essential terms for this Unit:

lurking variable
Simpson's Paradox

From Units B-1 and B-2 we also use:

conditional probability
dependent events
independent events

Conditional Probability

Conditional probability examines how the probability of an event changes if we know that another event has occurred. When the conditional probability is different from the overall probability of an event, the events are dependent. Two events are independent if when one occurs, the probability of the other remains unchanged.

Example - Dependence

Among male cigarette smokers, the risk of lung cancer is more than 20 times greater than among male nonsmokers, and it is 12 times greater for women smokers. Smoking contributes to many other diseases, such as coronary problems. The risks increase with the number of cigarettes and the length of time a person smokes. Now more people die prematurely from smoking than from auto accidents, alcohol abuse, drugs, and AIDS combined.
U.S. News and World Report Oct 19, 1998

Example - Independence

Engineers incorporate independent back-up systems to increase reliability. Satellites carry two onboard computers which operate independently; if the first fails, the second can perform the needed processing.

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