A college administration has conducted a study of 218 randomly selected students to determine the relationship between satisfaction with academic advisement and academic success. They obtained the following information: Of the 69 students on academic probation, 33 are not satisfied with advisement; however, only 28 of the students not on academic probation are dissatisfied with advisement. What is the probability that a student selected at random is not on academic probation and is not satisfied with advisement?

Question

anonymous · Answer

Probability of "not on academic probation" = (total students - probation students) / total students.

In other words, out of 218 students, how many were NOT on probation?  69 were on probation, so 218-69 were not on probation.  So the chance of choosing a student NOT on probation were (218-69)/218.

But for the other part of the problem, you still need to add up how many students were unhappy with advisement.  The number of students not satisfied with advisement divided by 218 is the probability that any particular student will be not satisfied...

The overall probability of choosing a student who was BOTH not on probation AND not satisfied with advisement is equal to the probability of choosing a student who was NOT on probation MULTIPLIED by the probability of choosing a student who was NOT satisfied with advisement.