Final answer:
The probability of events G and H being mutually exclusive is 0. The probability of events G and H being independent is not 0.15. The probability of the union of events G and H is 0.8.
Step-by-step explanation:
To find the probability of events G and H being mutually exclusive, we need to find the intersection of G and H, which represents the probability of both events occurring. Since G and H are mutually exclusive, their intersection is empty, meaning P(G ∩ H) = 0. So option a is the correct answer.
To find the probability of events G and H being independent, we need to compare P(G ∩ H) with P(G) × P(H). If the two probabilities are equal, then G and H are independent. However, since P(G ∩ H) = 0 and P(G) × P(H) = 0.15, G and H are not independent. So option c is the correct answer.
To find the probability of the union of events G and H, we need to find the probability of either G or H occurring (or both). Since G and H are mutually exclusive, the probability of either G or H occurring is the sum of their individual probabilities, P(G) + P(H) = 0.5 + 0.3 = 0.8. So option b is the correct answer.