Uniform Random Guesses

It is the dark ages. Imagine yourself seated at the game table inside a local tavern. You are exceptionally rich. Because this is so, you carry on your person an audacious coin purse to match your wealth. You anticipated a long night and therefore brought 100 coins of the following assortment:

[1]counterfeit:15

[2]copper: 30

[3]silver: 20

[4]gold: 10

[5]orichalcum:25

The man seated across from you would like to play a game. He will write 1 of the 5 names on a single note. If his guess matches a coin taken from your purse which has been fairly shaken to distribute the coins, then he wins. A recent decree has outlawed gambling for all the land since too many serfs were getting rich, he does not keep the coin.

If his guess is uniformly random, what is the probability that he loses?

Will he improve his chances of being correct by making the same guess repeatedly? If this is so, then which coin should he guess?

Explain your reasoning.

#Combinatorics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$