SOLUTION: Suppose that at any sitting of BUSI319, 35% of the students are first year; 30% are second year; 25% are final year and 10% are qualifying to enter various programs (assume mutuall

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Question 1166444: Suppose that at any sitting of BUSI319, 35% of the students are first year; 30% are second year; 25% are final year and 10% are qualifying to enter various programs (assume mutually exclusive). From records of the Statistics department, it was found that 20% of the first year students get A; 30% of the second year students get A; 35% of the final year students get A; 25% of the qualifying students get A. What is the probability a randomly chosen student will get an A? Given that a student got an A, what is the probability the student was first year? Second year? Third year? Qualifying?
Please help, thanks

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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Suppose that at any sitting of BUSI319, 35% of the students are first year; 30% are second year;
25% are final year and 10% are qualifying to enter various programs (assume mutually exclusive).
From records of the Statistics department, it was found that
20% of the first year students get A; 30% of the second year students get A;
35% of the final year students get A; 25% of the qualifying students get A. 

(a)  What is the probability a randomly chosen student will get an A? 

         P = 0.35*0.2 + 0.3*0.3 + 0.25*0.35 + 0.1*0.25.



(b)  Given that a student got an A, what is the probability the student was first year? 

        P = %280.35%2A0.2%29%2F%280.35%2A0.2+%2B+0.3%2A0.3+%2B+0.25%2A0.35+%2B+0.1%2A0.25%29.
     

(c)  Second year? 

        P = %280.3%2A0.3%29%2F%280.35%2A0.2+%2B+0.3%2A0.3+%2B+0.25%2A0.35+%2B+0.1%2A0.25%29.



(d)  Third year? 

        P = %280.25%2A0.35%29%2F%280.35%2A0.2+%2B+0.3%2A0.3+%2B+0.25%2A0.35+%2B+0.1%2A0.25%29.



(e)  Qualifying?

        P = %280.1%2A0.25%29%2F%280.35%2A0.2+%2B+0.3%2A0.3+%2B+0.25%2A0.35+%2B+0.1%2A0.25%29.


Solved.     //   All questions are answered.

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To develop further your knowledge and solving skills in elementary probability problems, look into the lessons
    - Simple and simplest probability problems
    - Solving probability problems using complementary probability
    - Elementary Probability problems related to combinations
    - A True/False test
    - A multiple choice answers test
    - Conditional probability problems
    - Typical probability problems from the archive
    - Experimental probability problems
    - Elementary operations on sets help solving Probability problems
in this site.

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