probability?

Question

An auditor checked the invoices prepared by three chain stores A, B and C. A sample of 200 invoices was selected. 80 were taken from store A,70 from B and 50 from C.The error rates of A, B and C were found to be 30% ,5% and 4% respectively. If one invoice was selected from the sample of 200 invoices, find the probability that
(a) it was from store A
(b)it contained an error
(c)it was from store B ,given that it contained an error.

Answer 1

a) 80 / 200 = 0.4
b) ( 80 * 0.3 + 70 * 0.05 + 50 * 0.04 ) / 200 = ( 24 + 3.5 + 2 ) / 200 = 0.1475.
c) 3.5 / (24 + 3.5 + 2 ) = 3.5 / 29.5 = 0.1186