Marinada '24

[lang=hr] Prilikom bacanja određene šesterostrane kockice s licima označenim brojevima $1$, $2$, $3$, $4$, $5$ i $6$, vjerojatnost dobivanja jedne strane, $F$ je veća od $1/6$, dok je vjerojatnost dobivanja nasuprotne strane od $F$ manja od $1/6$. Vjerojatnost dobivanja bilo koje od ostale četiri stranice je $1/6$, a zbroj brojeva na suprotnim stranicama je $7$. Kad se bace dvije takve kocke, vjerojatnost dobivanja zbroja od $7$ iznosi $\frac{47}{288}$. Kolika je vjerojatnost dobivanja lica $F$? [/lang] [lang=en] When rolling a certain unfair six-sided die with faces numbered $1$, $2$, $3$, $4$, $5$, and $6$, the probability of obtaining face $F$ is greater than $1/6$, the probability of obtaining the face opposite is less than $1/6$. The probability of obtaining any one of the other four faces is $1/6$, and the sum of the numbers on opposite faces is $7$. When two such dice are rolled, the probability of obtaining a sum of $7$ is $\frac{47}{288}$. What is the probability of obtaining face $F$? [/lang]