Final answer:
In handling mutually exclusive events q and r, with p(q) = 0.45 and p(r) = 0.30, the probability of either event occurring (p(q OR r)) is computed as 0.75, and the probability of both occurring together (p(q AND r)) is 0, owing to their mutual exclusivity.
Step-by-step explanation:
The question deals with the concept of mutually exclusive events in probability, specifically regarding events q and r. By definition, if events are mutually exclusive, the probability that they both happen at the same time is zero. As such, if we have that p(q) = 0.45 and p(r) = 0.30, several probabilities can be computed.
The probability of either event q or event r occurring, denoted as p(q OR r), is found by adding their individual probabilities: p(q) + p(r). We can solve this as follows:
- p(q OR r) = p(q) + p(r) = 0.45 + 0.30 = 0.75
Because events q and r are mutually exclusive, we can definitively state that:
- p(q AND r) = 0. Because they cannot occur together, their joint probability is zero.
Furthermore, it's important to note that these events being mutually exclusive also implies they're dependent events, not independent, since the occurrence of one entirely precludes the occurrence of the other.