Extract the Protractor

Amelia and Cory were seeking initiation to their local Magical Mathematical Society.

The leader had three protractors, two of which were clear-colored, and one of which was golden. The golden protractor was reputed to have mystical powers.

Both Amelia and Cory were to select a protractor blindfolded, and with thick gloves that prevented them being able to feel the difference between the clear and the golden.

What is the probability that neither Amelia nor Cory will get the golden protractor?

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