According to the U.S. Census Bureau, "only 35 percent of the foreign-born people in the United States in 1997 were naturalized citizens, compared with 64 percent in 1970" (Sacramento Bee, October 15, 1999, p. A1).
a. What is the probability that two randomly selected foreign-born people in the United States in 1997 were both naturalized citizens?
b. Refer to part (a) of this exercise. Suppose that a married couple was randomly selected instead of two separate individuals. Do you think the probability that they were both naturalized citizens would be the same as the probability in part (a)? Explain.
c. Do you think the probabilities reported by the Census Bureau are relative frequency probabilities or personal probabilities? Explain.
d. A student writing a report about these statistics wrote, "If you had lived in the United States in 1970 and were foreign-born, the probability that you would be a naturalized citizen would have been .64. But by 1997, if you still lived in the United States, the probability that you would be a naturalized citizen would be only .35." Rewrite this sentence in a way that conveys the information correctly.