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Joint Probability
Joint probability looks at the probability that two or more events will occur at the same time. It differs from conditional probability in that one event does not have to happen before the other - only that both will take place. An example of joint probability involves calculating the odds that a certain combination of numbers will result when two dice are rolled simultaneously. The probability of a given combination appearing is 1 out of 36 -- 6 sides times 6 sides equals 36 total possibilities.
Conditional Probability
Conditional probability looks at the probability that one event will occur after another has occurred. For example, conditional probability is indicated in the statement, "What are the odds that Event B will occur if Event A occurs first?" Conditional probability is so named because the ultimate chance of B happening is "conditioned" on A occurring. The partial knowledge that Event A happened alters the probability that Event B will also occur. There are two kinds of conditional probability: dependent and independent.
Conditional Dependent
Conditional dependent probability applies when the outcome of Event A directly alters the result of Event B. Taking the dice example; if the first die is thrown and one of the desired numbers comes up, then the odds that the second throw will produce the overall desired combination is now 1 in 6. The odds of the second throw are conditionally dependent on the result of the first roll.
Conditional Independent
Two events are independent if the occurrence of one has no effect on the other. This is still conditional probability because the odds of Event B are being calculated based on the result of Event A. However, because the events are truly independent, the probability of Event B based on Event A are the same as the probability of Event B occurring on its own. (