The percentage of mechanical-, civil-, aeronautical-, industrial-, and chemical-engineer- ing students in the course, Engineering Mathematics, is, respectively, 25, 20, 15, 22, and 18. The probability of a mechanical-, civil-, aeronautical-, industrial-, and chemical-en- gineering students getting the grade A is 0.7, 0.6, 0.8, 0.5, and 0.65, respectively. If a student chosen at random at the end of the semester earned an A in the course, find the probability of the student belonging to mechanical engineering.

Suppose 33.3% of high school students eat pizza and 42% drink soda. If 17.3% of high school students eat pizza and drink soda, what is the probability that a randomly chosen high student will either eat pizza, drink soda, or both?

Naturalization. The Office of Immigration Statistics collects and reports information about naturalized persons in the document U.S. Naturalizations. During one year, there were 694,193 persons who became naturalized citizens of the United States and, of those, 36%were originally from Asia. If 200 people who became naturalized citizens of the United States that year are selected at random, what is the probability that the number who were originally from Asia is a. fewer than 65? b. between 70 and 80, inclusive? c. less than 60 or more than 80?

. Assume that 75 percent of the students at the university have taken 4 years of high school math. Of those with four years of high school math, 80 percent plan to major in science. Of those without 4 years, only 10 percent plan to major in science. You stop a student at random. If the student plans to major in science, what is the probability that this student had four years of high school math?