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Question:

A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% defective computers and plant T2 produces 10% defective computers. If 60% of the computers produced are from plant T1, what is the percentage of defective computers produced by the factory?

3673

7893

4779

7583

Solution:

Let D1 be the percentage of defective computers produced by plant T1, and D2 be the percentage of defective computers produced by plant T2.
Let P1 be the percentage of computers produced by plant T1, and P2 be the percentage of computers produced by plant T2.
Given:
D1 = 20%
D2 = 10%
P1 = 60%
P2 = 100% - P1 = 100% - 60% = 40%
The percentage of defective computers produced by the factory is given by the weighted average of the defective percentages from each plant:
Percentage of defective computers = (P1 * D1) + (P2 * D2)
Percentage of defective computers = (60% * 20%) + (40% * 10%)
Percentage of defective computers = (0.60 * 0.20) + (0.40 * 0.10)
Percentage of defective computers = 0.12 + 0.04
Percentage of defective computers = 0.16
Therefore, the percentage of defective computers produced by the factory is 16%.