Question

4. The instructor for a large Stat 401 course surveys his students. He finds the following breakdown: 45% are Math majors(M), 39% are Statistics majors(St), and 16% are Actuarial Science majors(AS). Among the Math students, 60% indicate they will go to Grad School(G), while 80% of the Statistics students will go to Grad School, and only 10% of the Actuarial students will go to Grad School. a) Construct all of the probabilities given above, including conditional probabilities, using proper notation. 6pts b) Find the Probability of a randomly chosen student not going to Grad School. 2pts A calculation is sufficient here. c) Use Bayes’ Theorem, the version with Conditional Probabilities, to find the probability that a randomly chosen student who is going to Grad School is among the Statistics majors. Set up in Probability Notation and then substitute in numeric values. Use of a Tree Diagram will not receive credit.

Answer 1