Expert: Paul Klarreich - 12/3/2008

Question
13.) A biology class consist of 50 percent freshmen, 25 percent sophomores, 15 percent junior, and 10 percent seniors. Forty percent of the freshmen, 20 percent of the sophomores and junior, and 10 percent of the senior plan to go to medical school. a student is randomly selected from the class.
a) What is the probability that the student plans to go to medical school?

b) If the student selected plans to go to medical school, what is the probability that the student is a senior?

14.) In setting describe in Exercise 13, a student is randomly selected, and it is know that the student does not plan to go to medical school. What is most likely class standing of the student: freshman, sophomore, junior, or senior?

Answer
Questioner:   jason
Category:  Advanced Math
Private:  No
 
Subject:  finite math
Question:  

13.) A biology class consist of 50 percent freshmen, 25 percent sophomores, 15 percent junior, and 10 percent seniors. Forty percent of the freshmen, 20 percent of the sophomores and junior, and 10 percent of the senior plan to go to medical school.


a student is randomly selected from the class.

a) What is the probability that the student plans to go to medical school?

>> I think you can do this by just determining the number of students, class by class, who plan medical school.


b) If the student selected plans to go to medical school, what is the probability that the student is a senior?


>> Here, too, determine the number of seniors going to med school divided by the total in (a)


14.) In setting describe in Exercise 13, a student is randomly selected, and it is know that the student does not plan to go to medical school. What is most likely class standing of the student: freshman, sophomore, junior, or senior?


Now do the reverse -- you will know from (a) the number going, so you will know the number not going.  Now use the rule for conditional probability:

                              p(freshman AND not going)
p(freshman, given not going) = --------------------------
                                 p(not going)

-- same for other classes.