Naturalization. The U.S. Bureau of Citizenship and Immigration Services collects and reports information about naturalized persons in Statistical Yearbook. Following is an age distribution for persons naturalized during one year.

Age (yr) Frequency Age (yr) Frequency 18–19 5,958 45–49 42,820 20–24 50,905 50–54 32,574 25–29 58,829 55–59 25,534 30–34 64,735 60–64 18,767 35–39 69,844 65–74 25,528 40–44 57,834 75 & over 9,872 Suppose that one of these naturalized persons is selected at random.

a. Without using the general addition rule, determine the probability that the age of the person obtained is either between 30 and 64, inclusive, or at least 50.

b. Find the probability in part (a), using the general addition rule.

c. Which method did you find easier?