Question

An examination is attempted by five thousand graduates, two thousand post graduates and thousand doctorate holders .The probabilities that I graduate , a post graduate and a doctorate holder will pass the examination are ⅔,¾,⅘ respectively of one of the examinee passed the examination, then the probability that he is a post graduate is​

Answer 1

Given : An examination is attempted by five thousand graduates, two thousand post graduates and thousand doctorate holders .The probabilities that I graduate , a post graduate and a doctorate holder will pass the examination are ⅔,¾,⅘ respectively  

To find : one of the examinee passed the examination, then the probability that he is a post graduate is​

Solution:

Graduates appeared = 5000

passing Examination probability = 2/3

Expected passing candidates =  5000 * 2/3  = 10000/3

Post Graduates appeared = 2000

passing Examination probability =3/4

Expected passing candidates =  2000 * 3/4  = 1500

Doctorate holders appeared = 1000

passing Examination probability =4/5

Expected passing candidates =  1000 * 4/5  = 800

Total Expected passing candidates = 10000/3 + 1500 + 800

= 10000/3 + 2300

= 16900/3

one of the examinee passed the examination, then the probability that he is a post graduate is​  =  1500 / (16900/3)

= 4500 / 16900

=45/169

= 0.266

probability that he is a post graduate = 45/169 = 0.266

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