# [PHP], 71 bytes

With "include the empty string as a possible output".

<!-- language-all: lang-php -->

 while(0<$r=rand(0,9)/3){echo $r<0.1?'':str_repeat('p',round($r))."\n";}

[Try it online!][TIO-l0ec49es]

[PHP]: https://php.net/
[TIO-l0ec49es]: https://tio.run/##K8go@G9jXwAkyzMyc1I1DGxUimyLEvNSNAx0LDX1jTWrU5Mz8hVUimwM9Azt1dWtikuK4otSC1ITSzTUC9R1ivJLgWpVijQ19ZRi8pSsa///BwA "PHP – Try It Online"

-------------------
# [PHP], 52 bytes

<!-- language-all: lang-php -->

 while(0<$r=rand(0,9)){echo str_repeat('p',$r)."\n";}

[Try it online!][TIO-l0ec0fe1]

[PHP]: https://php.net/
[TIO-l0ec0fe1]: https://tio.run/##K8go@G9jXwAkyzMyc1I1DGxUimyLEvNSNAx0LDU1q1OTM/IVikuK4otSC1ITSzTUC9R1VIo09ZRi8pSsa///BwA "PHP – Try It Online"