Final answer:
To calculate the probability of either event A or event B occurring, we use different formulas based on whether the events are mutually exclusive or independent. For mutually exclusive events, the probability is the sum of the probabilities of each event. For independent events, it is the sum minus the probability of them both occurring simultaneously.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focused on the topic of probability relating to independent and mutually exclusive events.
Part (a): Mutually Exclusive Events
If events A and B are mutually exclusive, no outcome can belong to both events at the same time, which implies that P(A AND B) = 0. Therefore, the probability of either A or B occurring is simply P(A OR B) = P(A) + P(B), which in the given numbers would be P(A OR B) = 0.29 + 0.22 = 0.51.
Part (b): Independent Events
If events A and B are independent, the occurrence of one event has no effect on the probability of the other event occurring. The probability of either event occurring is given by P(A OR B) = P(A) + P(B) - P(A AND B). Since the two events are independent, P(A AND B) is equal to P(A)P(B), which would be 0.29 * 0.22 = 0.0638. Therefore, P(A OR B) = 0.29 + 0.22 - 0.0638 = 0.4462.