A computer monitor manufacturer subcontracts its major parts to four vendors: A$,$ B$,$ C$,$ and D$.$ Past records show that vendors A and C provide $30\%$ of the requirements each, vendor B provides $25\%,$ and vendor D provides $15\%.$ In a random sample of $10$ parts, $4$ were found to be nonconforming. It is known that vendors A and C operate at a level of $5\%$ nonconformance rate, while vendors B and D are at $10\%$ and $15\%,$ respectively. What is the probability that the sample came from vendor A$?$ From vendor B$?$ From vendor C$?$