The Atlantic Hurricane Database extends back to 1851, recording among other things the number of major hurricanes striking the U.S. Atlantic and Gulf Coast per year. A major hurricane is a hurricane measuring at least a Category 3 on the Saffir-Simpson hurricane wind scale (i.e., with winds of at least 110 mph). As published by the National Oceanic & Atmospheric Administration and the Atlantic Oceanographic & Meteorological Laboratory, the following table provides a probability distribution for the number of major hurricanes, Y , for a randomly selected year between 1851 and 2012.

Use random-variable notation to represent each of the following events. The year had
a. At least one major hurricane.
b. Exactly three major hurricanes.
c. Between 2 and 4 major hurricanes, inclusive.
Use the special addition rule and the probability distribution to determine
d. P(Y ≥ 1).
e. P(Y = 3).
f. P(2 ≤ Y ≤ 4).

0 0.185 5 0.056 0.296 6 0.037 2 0.266 70.012 30.093 8 0.006 40.049