Question

A college administration has conducted a study of 190randomly selected students to determine the relationship between satisfaction with academic advisement and academic success. They obtained the following​ information: Of the 68students on academic​ probation, 34are not satisfied with​ advisement; however, only 25of the students not on academic probation are dissatisfied with advisement. What is the probability that a student selected at random is onacademic probation and is not satisfiedwith​ advisement?

Answer 1

The probability that a student selected at random is on academic probation and is not satisfied with​ advisement is 0.1789

Explanation:

Consider the provided information.

Out of 68 students on academic​ probation, 34 are not satisfied with​ advisement; That means 68-34=34 are satisfied with advisement.

If 68 students are in academic then the non academic students probation will be: 190-68=122

Only 25of the students not on academic probation are dissatisfied with advisement.

That means 122-25=97 students are satisfied.

According to the provided information draw the table as shown.

Satisfied Not satisfied Total

Academic probation 34 34 68

Non academic probation 97 25 122

Total 131 59 190

Now we need to determine the probability that a student selected at random is on academic probation and is not satisfied with​ advisement.

On academic probation and is not satisfied with​ advisement = 34

The total number of cases is 200.

`Probability=\frac{\text{Favourable cases}}{\text{Total number of cases}}`

Substitute the respective values:

`Probability=(34)/(190)\approx 0.1789`

Hence, the probability that a student selected at random is on academic probation and is not satisfied with​ advisement is 0.1789