Question 466673: One probability class of 30 students contains 15 that are good, 10 that are fair, and 5 that are of poor quality. A second probability class, also of 30 students, contains 5 that are good, 10 that are fair, and 15 that are poor. You (the expert) are aware of these numbers, but you have no idea which class is which. If you examine one student selected at ranŽdom from each class and find that the student from class A is a fair student whereas the student from class B is a poor student, what is the probability that class A is the superiŽor class?
i think that P(to chose a fair student from class A) = 10/30 = 1/3,
and P(to chose a poor student from class B) = 15/30 = 1/2.
Now i am not sure how to calculate the P(that A is the superior class)... 1/3 * 1/2 maybe???
thanks a lot
Answer by sudhanshu_kmr(1152)   (Show Source):
You can put this solution on YOUR website!
Use Bye's theorem of probability.
Superior : 15 are good, 10 are fair, and 5 are poor
other : 5 are good, 10 are fair, and 15 are poor.
Probability that fair from superior and poor from other = 10/30 * 15/30 = 1/6
probability that fair from other and poor from superior : 10/30 * 5/30 = 1/18
required probability = (1/6) / [ 1/6 + 1/18]
= (1/6) / [4/18]
= 3/4
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