Question

In a class of 75 students,15 are above average,45 are average and the rest below average achievers.The probability that an above average achieving student fails is 0.005,then an average achieving student fails is 0.05 and the probability of a below average achieving student failing is 0.15.If a student is known to have passed,what is the probability that he is a below average achiever?

Answer 1

let O be over average, A be average, and B be below average, F for fail and P for pass
prob(O) = 15/75 = 1/5
prob(A) = 45/75 = 3/5
prob(B) = 15/45 = 1/5
prob(P) = x
prob(F) = 1-x , not really needed

so we have
AF = .05
AP = (3/5)x
OF = .005
OP = (1/5)x
BF = .15
BP = (1/5)x

.05 + 3x/5 + .005 + x/5 + .15 + x/5= 1
x = 1 - .05 - .005 - .15 = .795

Thus:
AF = .05
AP = .477
OF = .005
OP = .159
BF = .15
BP = .159 , notice they add up to 1

So we have BP = .159
B(.795) = .159
B = .159/.795 = .2