Explanation
In probability theory, a conditional probability is the likelihood of an event occurring given that another event has already occurred. This is denoted as , which reads as the probability of given .
Key Formula:
Where:
- is the conditional probability of event occurring given event .
- is the joint probability of both events and occurring.
- is the probability of event occurring.
Given Situations
- The probability that your team wins the championship given that you go to the finals is a conditional probability because it is based on the condition that you have reached the finals.
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The probability that you are given a bike for your birthday is simpler and is not based on another event. Hence, it is not a conditional probability.
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The probability that you roll a 1 on a number cube is an independent probability event and doesn't depend on any prior condition, so it is not conditional.
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The probability that your team wins the championship generally, without any extra information, is not conditional since it doesn't depend on another prior event.