SOLUTION: THis question is coming from Quantitive Methods and concerns Marginal and Joint probability. It is a 2 part question. I completely do not understand how to solve this problem. I do

Question 225375: THis question is coming from Quantitive Methods and concerns Marginal and Joint probability. It is a 2 part question. I completely do not understand how to solve this problem. I do not understand how to formulate to solve:
"A metro school system consists of 2 districts: north and south. The north district contains 60% of all students and the south district contains 40% of all students. A competency test was given to all students. 10% of the north district failed and 15% of the south district failed."
Question A: What is the probability that a student from the entire school system, chosen at random, has passed?
Question B using Bayes Rule: What is the probability that a student who has failed the test came from the South District?
Any help is learning how to EASILY formulate and solve would be appreciated. Thanks!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
working with a numerical example makes this more straight forward

say 1000 students in the system

"The north district contains 60% of all students" ___ (60%)1000 = 600

"the south district contains 40% of all students" ___ (40%)1000 = 400

"10% of the north district failed" ___ (10%)600 = 60

"15% of the south district failed" ___ (15%)400 = 60

A: 120 out of 1000 failed, so 880 passed (1000-120)
___ probability of a student from the system passing is 880/1000 or .88

B: 120 failed and 60 of those came from South
___ probability of a failed student from South is 60/120 or .5
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