A sequence of Bernoulli trials consists of choosing components at random from a batch of components. A selected component is classified as either defective or non-defective. A non-defective component is considered a success, while a defective component is considered a failure. If the probability that a selected component is non-defective is 0.8, determine the probabilities of the following events:
a. The first success occurs on the fifth trial.
b. The third success occurs on the eighth trial.
c. There are 2 successes by the fourth trial, there are 4 successes by the tenth trial, and there are 10 successes by the eighteenth trial.