Mana LaTeX yordamida isbot: $x$ va $y$ ikkita tasodifiy butun son bo'lsin. $xy$ ko'paytmasi, agar va faqat $x$ va $y$ juft yoki $x$ va $y$ juft bo'lsa, juft bo'ladi. $x$ juft bo'lish ehtimoli $\frac{1}{2}$ va $x$ juft bo'lish ehtimoli ham $\frac{1}{2}$. Xuddi shunday fikrlash orqali, $y$ juft bo'lish ehtimoli \frac{1}{2}$ va $y$ juft bo'lish ehtimoli $\frac{1}{2}$. Shuning uchun $x$ va $y$ juft bo'lish ehtimoli yoki $x$ va $y$ juft bo'lish ehtimo
spam fails_task lang_mismatch pii not_appropriate hate_speech sexual_content quality toxicity humor helpfulness creativity violence