Major Hurricanes. 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 SaffirSimpson 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.

y P(Y = y) y P(Y = y)

0 0.185 5 0.056 1 0.296 6 0.037 2 0.266 7 0.012 3 0.093 8 0.006 4 0.049 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).