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Unconditional Vs Conditional Probabilities

Unconditional Vs Conditional Probabilities

Unconditional probability (also known as marginal probability) is simply the probability that an event occurs without considering any other preceding events. In other words, unconditional probabilities are not dependent on the occurrence of any other events; they are ‘stand-alone’ events. Therefore, if we are interested in the probability of an event, say, A, the standard annotation is P (A). Let us look at a few examples.

  1. The probability that it will rain on a given day without considering the rainfall pattern of a given area or any other climatic factor.
  2. The probability that a given stock will earn a 10% annual return without considering the preceding annual returns.

Conditional Probability

A conditional probability is the exact opposite of an unconditional probability. Our interest lies in the probability of an event ‘A’ given that another event ‘B ‘ has already occurred. This is what you should ask yourself:

“What is the probability of one event occurring if another event has already taken place?

We pronounce P (A | B) as “the probability of A given B.”

The bar sandwiched between A and B indicates “given.”

Examples

  1. What is the probability that it will rain on a given day, given that there have been rains on each of the 3 preceding days?
  2. The probability that a stock will earn a 10% annual return, given that it has earned a 9% return during each of the two previous financial years.

Understanding the theory behind conditional and unconditional probabilities will help you understand and work out solutions for quantitative probability questions.


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