According to the article "Characterizing the Severity and Risk of Drought in the Poudre River, Colorado" (J. of Water Res. Planning and Mgmnt., 2005: 383-393), the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). The cited paper proposes a geometric distribution with p = .409 for this random variable.
a. What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?