DEFINITION of 'Compound Probability'
A mathematical term relating to the likeliness of two independent events occurring. The compound probability is equal to the probability of the first event multiplied by the probability of the second event. Compound probabilities are used by insurance underwriters to assess risks and assign premiums to various insurance products.
INVESTOPEDIA EXPLAINS 'Compound Probability'
The most basic example of compound probability is flipping a coin twice. If the probability of getting heads is 50% (.50), then the chances of getting heads twice in a row would be (.50 X .50), or .25 (25%).
As it relates to insurance, underwriters may wish to know, for example, if both members of a married couple will reach the age of 75, given their independent probabilities. Or, the underwriter may want to know the odds that two major hurricanes hit a given geographical region within a certain time frame. The results of their math will determine how much to charge for insuring people or property.

Conditional Probability
Probability of an event or outcome based on the occurrence of ... 
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Actuary
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