Final answer:
Mutually exclusive eventsG and H cannot occur simultaneously, which is why the statement P(H|G) = 0.4 must be false. P(H OR G) is calculated to be 0.8. G and H are dependent events since the occurrence of one affects the possibility of the other.
Step-by-step explanation:
When events G and H are mutually exclusive, it means they cannot occur at the same time.
Therefore, the probability of event H occurring given that event G has already occurred, denoted as P(H|G), must be 0 because once event G has happened, there is no chance for event H to occur. This directly contradicts the statement P(H|G) = 0.4, making it false.
To find P(H OR G), we use the addition rule for mutually exclusive events, which is P(H) + P(G), giving us 0.3 + 0.5 = 0.8. Finally, events G and H are dependent events because the occurrence of one event completely rules out the occurrence of the other event.