Conditional Probabilities. Please show your work for each question

Approximately 90% of US high school graduate! attended public school and 10% private school. Among public school graduates, roughly 2/3 enrolled in college, of whom 1/3 enrolled directly in fouryear colleges and 2/3 in twoyear colleges. Among private school graduates, about 95% enrolled in four year colleges and the remaining 5% in twoyear colleges. a) (4 pts) Illustrate this situation with a tree diagram. At each branching, indicate the probability of following each branch. b) (2 pts) Compute the fraction of public high school graduates who enroll in a fouryear college. c) (3 pts) Compute the fraction of all high school graduates who graduate from public school and then enroll in a fouryear college. d) (3 pts) Compute the fraction of all high school graduates who enroll in a fouryear college. e) (3 pts) Using these data, compute the fraction of beginning students at fouryear colleges (ig noring other situations like international students, transfer students, homeschooled students, etc) who graduated from public high schools. Be sure to show your work and explain your reasoning. (There is more than one way to do this.)