Let E = Event of choosing defective shirt. A = Event of choosing defective shirt from process A Similarly B and C be the event choosing shirt from process B and C. Now, P(A) =
25
100
, P(B) =
35
100
, P(C) =
40
100
P(E/A) =
5
100
, P(E/B) =
4
100
, P(E/C) =
2
100
Now, by Baye's theorem,
P(C/E) =
P(E∕C)⋅P(C)
P(E∕A)⋅P(A)+P(E∕B)⋅P(B)+P(E∕C)⋅P(C)
=
2
100
×
40
100
5
100
×
25
100
+
4
100
×
35
100
+
2
100
×
40
100
=
80
125+140+80
=
80
345
=
16
69
Probability of defective shirt selected from process C is