I attempted to answer this question but I can't seem to understand why my reasoning it wrong. Looking at the back of the book makes a little sense but I don't know if its the wording or my understanding:

(Note: THis is question 63 from OG Orange book on page 206):

A computer ship manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What is the defective chips in a shipment of 60,000 chips?

The table (badly formatted):

Shipment; Number of defective chips; Total number of chips
S1; 2; 5,000
S2; 5; 12,000
S3; 6; 18,000
S4; 4; 16,000

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The way I was going about it was that because it states that the ratio is S1+S2+S3+S4 combined, I was calculating each ratio individually and trying to add them up like this:

2/5000 + 5/12000 + 6/18000 + 4/16000

Then I went added and multipled the number by 60K. (note: the answer wasn't found which means I was way off).

Now, the answer states that I should have added the ratios differently like this:

(2+5+6+4)/(5000 + 12000 + 18000 + 16000) to give me an answer of 20.

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Where am I wrong here? Isn't a combined ratio just adding up all the ratios of the individual pieces? What does adding up ratios of individual pieces mean exactly (or does it even mean anything?) - ?

Let me know your thoughts.