What happens to the probability when two independent events are combined?

When two independent events are combined, the probability of both events occurring is determined by multiplying their individual probabilities. This principle arises from the definition of independent events, where the occurrence of one event does not influence the occurrence of the other.

For instance, if Event A has a probability of ( P(A) ) and Event B has a probability of ( P(B) ), the probability of both events A and B happening together is calculated as:

[ P(A \text{ and } B) = P(A) \times P(B) ]

This multiplication reflects the likelihood of both events occurring simultaneously, effectively combining their probabilities while taking into account their independence.

Thus, option C accurately describes the correct method for finding the probability of two independent events happening together.