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The HP Photosmart Premium All-in-One printer can be used as a printer, copier, scanner. This printer uses a 5 color print system.

Why are there two black cartridges? Thin left, Thick right?

I replaced the thick one of the far right of the think black one and thin color ones. It is 100% full.

My guess is that the system is selecting the thin black cartridge on the left, which is almost empty.

How can I have it select the the thicker black cartridge on the right?

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COMPLETION ANSWER

You have a Photo Black (PK) model; the 309g is a 5-color photo printer, HP later got rid of this even on the Photosmart models and reduced them to 4 color CMYK and their photo range took a nosedive :-(. The Photo Black is only used for photo printing, which is why it doesn't cause issues with day-to-day printing.

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