Question

A car manufacturer receives its air conditioning units from 3 different suppliers, A; B; C.

25% of its units come from supplier A, 26% from supplier B and 49% from supplier

C .It is known that 8% of the units from supplier A are defective, 8% of units from

supplier B are defective and 5% of units from supplier C is defective. If a unit is

selected at random and is found to be defective, what is the probability that it came

from Supplier A?

Answer 1

probability of defective =came from A and defective+came from B and defective+came from C and defective

$= 0.25 \times 0.08 +0.26 \times 0.08 + 0.49 \times 0.05 \\ = 0.02 + 0.0208 + 0.0245 \\ = 0.0653$

P(from A| defective) $= \frac{0.5 \times 0.08}{0.0653}= 0.3062$