60% of the student body at utc is from the state of tennessee (t), 30% are from other states (o), and the remainder constitutes international students (i). twenty percent of students from tennessee lives in the dormitories, whereas, 50% of students from other states live in the dormitories. finally, 80% of the international students live in the dormitories. given that a student does not live in the dormitory, what is the probability that he/she is an international student?

0.0308

Step-by-step explanation:

Let as consider

T : Student lives in state of Tennessee

O : Student lives in state of other states

I : Student is an international students

D: Students live in the dormitories.

From the given information it is clear that

Using conditional probability:

If a student does not live in the dormitory, then we need to find the probability that he/she is an international student.

We know that

The probability that student live in the dormitories is

The probability that student does not live in the dormitories is

If a student does not live in the dormitory, then the probability that he/she is an international student is

Therefore, the required probability is 0.0308.

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