3.113 A dean has found that 62% of entering freshmen and 78% of community college transfers eventually graduate. Of all entering students, 73% are entering freshmen and the remainder are community college transfers.

a. What is the probability that a randomly chosen entering student is an entering freshman who will eventually graduate?

b. Find the probability that a randomly chosen entering student will eventually graduate.

c. What is the probability that a randomly chosen entering student either is an entering freshman or will eventually graduate (or both)?

d. Are the events “eventually graduates” and “enters as community college transfer” statistically independent?