Bring home a Diamond

A contestant on the game show "A Diamond for your Wife" gets to select 5 diamonds from a box. The box contains 20 diamonds of which 8 are fakes.

Regardless of how many real diamonds the contestant has after his selection, he can only take one home to his wife. A second contestant then gets to select from the remaining 15 diamonds in the box but he can select only 1.

What is the probability that this second contestant selects a real diamond?

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