Final answer:
The type of probability that considers the likelihood of an event 'given that' another event has occurred is called conditional probability, denoted as P(A|B). The correct answer is A.
Step-by-step explanation:
The type of probability that looks at the probability of an event happening 'given that' another event has occurred is known as conditional probability. Conditional probability is denoted as P(A|B), which means 'the probability of event A occurring given that event B has already occurred'. This concept is crucial in situations where the outcome of one event affects the outcome of another, making them dependent events.
To calculate conditional probability, we use the formula P(A|B) = P(A AND B) / P(B), where P(B) must be greater than zero. This formula allows us to focus on a reduced sample space that only considers the occurrence of event B. An example of applying conditional probability could be determining the probability that a hiker prefers mountainous trails, given that they have already expressed a preference for hiking near lakes and streams.
Conditional probability is different from joint probability (which is the probability of two events occurring together), marginal probability (the probability of a single event without consideration of other events), and independent probability (the probability of an event that is not affected by other events).