ms-08 mba assignment july dec 2010 Question 2

2. Among the examinees in an examination 30%, 35% and  45% failed in Statistics, in Mathematics, and in at least one of the subjects respectively. An examinee is selected at random. Find the probabilities that

a.        He failed in Mathematics only

b.        He passed in Statistics, if it is known that he has failed in Mathematics

Solution:

Given: P (failed in statistics) = P(S.F) = 30%  = 30/100 = 0.3

            P (failed in maths) = P (M.F) = 35% = 35/100 = 0.35

            P (passed in Statistics) = P (S.P) = 100 – 30 = 70% = 0.70

            P (Failed in atleast one subject) = P (S.F U M.F) = 45%

                                                               = 45/100 = 0.45

(a)  To find P (failed in Maths only)                                                                                           

P (S.F U M.F) = P (S.F)  + P (M.F) – P ( S.F  M.F)

P ( S.F INERTSECTION M.F) = 0.3 + 0.35 – 0.45

                                                   = 0.20

P (failed in maths only) = P (M.F) – P(S.F  M.F)

                                       = 0.35-0.20 = 0.15

(b) To find P( passed in statistics if known  failed in maths)

           = P (failed in maths) and P ( passed in statistics)

           = 0.35 * 0.70 = 0.245