Final answer:
The question involves calculating probabilities of independent and mutually exclusive events within the subject of mathematics.
Step-by-step explanation:
The question asks to understand concepts in probability regarding independent and mutually exclusive events. Mutually exclusive events cannot occur at the same time, which means that the probability of both events happening together is zero (P(A AND B) = 0). For independent events, the occurrence of one event does not affect the probability of the other occurring (P(A AND B) = P(A)P(B)).
An example is given with events U and V being mutually exclusive with specific probabilities assigned to each. The question related to the probability of their union and intersection is to demonstrate understanding of the basic probability rules for these types of events.