At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state. All students must take and pass an Entry Level Math (ELM) test. We also know that if from south, 60% of students have passed the test. If from north, 70% have passed the test, and if from out-of-state, 90% of students have passed the test.

1) List the probability distribution table (Use P,P respectively for Pass /no Pass, and use N, S, O, for north, south, and out-of state)

2) If a randomly selected student has passed the test, what is the probability that the student is from out-of-state?

3) What is the probability that a randomly selected student is not from southern Texas and has not passed the test?

4) If a randomly selected student has not passed, what is the probability that the student is not from northern Texas?

5) If a randomly selected student is not from out-of-state, what is the probability that the student has passed?