Question

90 percent students of a Class are well prepared and 10 percent
unprepared for an examination in Mathematics. If the
probability of passing with preparedness is 0.85 and that of not
passing with unpreparedness is 0.60, find the probability that a
student selected at random :
Who is found to have passed must have been well prepared.
Who is found to have failed must have been unprepared.​

Answer 1

Given : 90 percent students of a Class are well prepared and 10 percent

unprepared for an examination in Mathematics.  the  probability of passing with preparedness is 0.85 and that of not  passing with unpreparedness is 0.60,

To find :  the probability that a  student selected at random :

(i) Who is found to have passed must have been well prepared.

(ii) Who is found to have failed must have been unprepared.​

Solution:

Well prepared   =  90  % = 0.9

unprepared  =  10 %  = 0.1

probability of passing with preparedness is 0.85

probability  not passing with unpreparedness is 0.60

Well prepared  passing = 0.9 * 0.85  =  0.765

Well prepared not passing = 0.9 * (1 - 0.85)  = 0.135

unprepared  passing = 0.1 * (1 - 0.6)  =  0.04

unprepared  not passing = 0.1 * ( 0.6)  =  0.06

probability that a student selected at random found to have passed must have been well prepared.    = passes well prepared / total passed

  0.765 / ( 0.765 + 0.04)

= 0.765/0.805

= 0.9503

= 95.03 %

probability that a student selected at random found to have failed must have been unprepared.​   = unprepared failed / total failed

=  0.06 / (0.06 + 0.135)

= 0.06/ 0.195

= 0.3077

= 30.77 %

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