Most students ignore this chapter. The problems here involve Borel-Cantelli lemmas and advanced expectation tricks that reappear in Chapter 8 (Brownian motion). A good solution set for Chapter 1 should show you how to handle "indicator variable" splitting—Ross’s favorite technique.
Some solutions (and the text itself) can be heavy on calculation rather than conceptual shorter proofs, which may frustrate those looking for purely theoretical elegance. Mathematics Stack Exchange