SOLUTION: 7. In a class of advanced statistics, there are 10 first- year, 30 second year and 10 third- year students. The final examination results reveal that 3 first- year, 10 second- ye

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Question 1194271: 7. In a class of advanced statistics, there are 10 first- year, 30 second year and 10 third- year
students. The final examination results reveal that 3 first- year, 10 second- year and 5 third- year
students received an A for the course. If a student from this class is selected at random and found
to get A, what is the probability that he was a second year student?
Answer by ikleyn(53937) About Me  (Show Source):
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7. In a class of advanced statistics, there are 10 first- year, 30 second year and
10 third- year students. The final examination results reveal that 3 first- year,
10 second- year and 5 third- year students received an A for the course.
If a student from this class is selected at random and found
to get A, what is the probability that he was a second year student?
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    It is  P = 10%2F%283+%2B+10+%2B+5%29 = 10%2F18 = 5%2F9.    ANSWER


Working with the conditional probability problems, we can reduce the space of events, 
considering the events under the imposed condition.


Then the denominator of the probability fraction is the number of elements
in the reduced space, while the numerator is the number of favorable elements
in this reduced space of events.

Solved and explained.