Unconditional Probability: Overview and Examples

What Is Unconditional Probability?

An unconditional probability is the chance that a single outcome results among several possible outcomes. The term refers to the likelihood that an event will take place irrespective of whether any other events have taken place or any other conditions are present.

The probability that snow will fall in Jackson, Wyoming, on Groundhog Day, without taking into consideration the historical weather patterns and climate data for northwestern Wyoming in early February is an example of an unconditional probability.

Unconditional probability may be contrasted with conditional probability.

Key Takeaways

  • Unconditional probability reflects the chance that some event will occur without accounting for any other possible influences or prior outcomes.
  • For instance, the chance of a fair coin flip being heads has an unconditional probability of 50% regardless of how many coin flips preceded it, nor if some other event had occurred.
  • Unconditional probability is also known as marginal probability.

Understanding Unconditional Probability

The unconditional probability of an event can be determined by adding up the outcomes of the event and dividing by the total number of possible outcomes.

 P ( A )   =   Number of Times ‘ A ’ Occurs Total Number of Possible Outcomes P(A)\ =\ \frac{\text{Number of Times `}A\text{' Occurs}}{\text{Total Number of Possible Outcomes}} P(A) = Total Number of Possible OutcomesNumber of Times ‘A’ Occurs

Unconditional probability is also known as marginal probability and measures the chance of an occurrence ignoring any knowledge gained from previous or external events. Since this probability ignores new information, it remains constant.

Conditional probability, on the other hand, is the likelihood of an event or outcome occurring, but based on the occurrence of some other event or prior outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

Conditional probability is often portrayed as the "probability of A given B," notated as P(A|B). Unconditional probability also differs from joint probability, which calculates the likelihood of two or more outcomes occurring simultaneously, and portrayed as the "probability of A and B", written as P(A ∩ B). It essentially incorporates the unconditional probabilities of A and B.

Example of Unconditional Probability

As a hypothetical example from finance, let's examine a group of stocks and their returns. A stock can either be a winner, which earns a positive return, or a loser, which has a negative returns. Say that out of five stocks, stocks A and B are winners, while stocks C, D, and E are losers. What, then, is the unconditional probability of choosing a winning stock? Since two outcomes out of a possible five will produce a winner, the unconditional probability is 2 successes divided by 5 total outcomes (2 / 5 = 0.4), or 40%.

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