A certain item is produced in a factory on one of three mach

A certain item is produced in a factory on one of three machines,
A, B, or C. The percentages of items produced on machines A, B, and
C, are 50%; 30%; and 20% respectively. Moreover, 4% of A\'s products ,
2% of B\'s products, and 4% of C\'s products, respectively, are defective.
What is the percentage of all copies of this item that are defective?

Solution

P(A) = 0.50, P(B) = 0.30, P(C) = 0.20

4% of A\'s Products are defective = 4 * 0.50/100 = 0.02
2% of B\'s Products are defective = 2 * 0.30/100 = 0.006
4% of C\'s Products are defective = 4 * 0.20/100 = 0.008

percentage of all copies of this item that are defective = 0.02+0.06+0.08 = 0.034

3.4% items are defective