In a school in florida, 60% of the students stay in the school's dormitory and 40% stay with their families. the school records show that 30% of the students living in the dormitory and 20% of the students living with their families obtain as on exams. if a student chosen at random from the school receives as, the probability that the student lives in the school dormitory is a. 1/26 b. 1/18 c. 9/26 d. 9/13

We have events:

- a student stays in the school's dormitory
- a student stays with family
- a student receives As

and  probabilities:



We want to calculate the probability that the student lives in the school dormitory given he receives As so it will be . From the Bayes' theorem we know that:



The only thing we don't know is , but we can calculate it using the law of total probability. There will be:



So our probability:



Answer D.