Final answer:
The questions are related to calculating probabilities, including finding specific event probabilities, understanding conditional probabilities, and using principles such as the additive and multiplicative rules and complements in probability theory within mathematics.
Step-by-step explanation:
The question involves calculating probabilities in different scenarios, which is a common task in probability theory, a branch of mathematics. For example, when calculating the probability that a person is female or prefers hiking on mountain peaks (F for female and P for prefers mountain peaks), one would need to find P(F) for the probability of being female, P(P) for the probability of preferring mountain peaks, P(F AND P) for the probability of both being female and preferring mountain peaks, and P(F OR P) for the probability of being either female or preferring mountain peaks. Additionally, understanding conditional probabilities, such as P(A|B), which is the probability of event A given that event B has occurred, is crucial.
Calculating conditional probabilities like P(B|A) as well as computing probabilities of independent and mutually exclusive events are also part of the tasks. Moreover, one must be aware of the complement rule to find the probability of the complement of an event, as in P(B') = 1 - P(B), where B' is the complement of event B (meaning the event that B does not occur).
In summary, to solve these problems, one must apply principles of probability including the additive and multiplicative rules, the use of complements, and the concept of conditional probability.