Final answer:
To prove that events G and H are independent, one must show that P(G AND H) is equal to P(G) multiplied by P(H), or that P(H|G) equals P(H). Given values satisfy the multiplicative condition, showing that the events are independent.
Step-by-step explanation:
The question being asked is a mathematical one, involving the concept of probability and whether two events are independent. To show that events G and H are independent, we need to prove that the probability of one event occurring does not affect the probability of the other event occurring. In this case, if the probability of taking a math class (P(G)) is 0.6 and the probability of taking a science class (P(H)) is 0.5, then these events are independent if the probability of taking both a math and science class (P(G AND H)) is the product of P(G) and P(H), which would be 0.6 * 0.5 = 0.3, as given. Furthermore, we can also show independence by demonstrating that the conditional probability of H given G (P(H|G)) equals P(H), indicating that knowing someone is taking a math class does not change the probability they are also taking a science class.