Zsh, 19 bytes

grep -oam1 x /*/ur*

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Explanation:

• /*/ur*: glob for /dev/urandom, a random infinite stream of bytes
• grep x: search for the letter x
• -o: print only the letter xs
• -a: force output even though /dev/urandom is a binary file
• -m1: quit after the first matching line

Pure Zsh, 20 bytes

for ((;RANDOM;))<<<x

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Loop breaks with probability \$ \frac 1 {32768} \$ for each iteration.

Explanation:

• for ((;RANDOM;)): loop while $RANDOM (which is a random integer in the range \$ [0, 32768) \$, is nonzero
• <<<x: print x

Here's a version for 2 bytes more with a probability of \$ \frac 1 2 \$, and is much more easy to demonstrate:

for ((;RANDOM%2;))<<<x

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Zsh, 19 bytes

grep -oam1 x /*/ur*

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Explanation:

• /*/ur*: glob for /dev/urandom, an infinite stream of random bytes
• grep x: search for the letter x
• -o: print only the letter xs
• -a: force output even though /dev/urandom is a binary file
• -m1: quit after the first matching line

Pure Zsh, 20 bytes

for ((;RANDOM;))<<<x

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Loop breaks with probability \$ \frac 1 {32768} \$ for each iteration.

Explanation:

• for ((;RANDOM;)): loop while $RANDOM (which is a random integer in the range \$ [0, 32768) \$, is nonzero
• <<<x: print x

Here's a version for 2 bytes more with a probability of \$ \frac 1 2 \$, and is much more easy to demonstrate:

for ((;RANDOM%2;))<<<x

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Zsh, 19 bytes

grep -oam1 x /*/ur*

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Pure Zsh, 20 bytes

for ((;RANDOM;))<<<x

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Loop breaks with probability \$ \frac 1 {32768} \$ for each iteration.

Here's a version for 2 bytes more with a probability of \$ \frac 1 2 \$, and is much more easy to demonstrate:

for ((;RANDOM%2;))<<<x

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Zsh, 19 bytes

grep -oam1 x /*/ur*

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Explanation:

• /*/ur*: glob for /dev/urandom, a random infinite stream of bytes
• grep x: search for the letter x
• -o: print only the letter xs
• -a: force output even though /dev/urandom is a binary file
• -m1: quit after the first matching line

Pure Zsh, 20 bytes

for ((;RANDOM;))<<<x

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Loop breaks with probability \$ \frac 1 {32768} \$ for each iteration.

Explanation:

• for ((;RANDOM;)): loop while $RANDOM (which is a random integer in the range \$ [0, 32768) \$, is nonzero
• <<<x: print x

Here's a version for 2 bytes more with a probability of \$ \frac 1 2 \$, and is much more easy to demonstrate:

for ((;RANDOM%2;))<<<x

Attempt This Online!