Marinada '25

[lang=hr] Martin je zarobljen u Matejevoj MNM sobi i želi izaći van. Pred njim su troja vrata. Prva vode do prolaza kojim nakon $2$ minute izlazi van. Druga vrata vode do tunela kojim se vraća na početak nakon $3$ minute. Treća vode do tunela koji ga vraća na isto mjesto nakon $5$ minuta. Uz pretpostavku da svaki put s jednakom vjerojatnošću bira bilo koja vrata, odredite očekivano vrijeme do izlaska iz Matejeve MNM sobe. [/lang] [lang=en] Martin is trapped in Matej’s MNM room and wants to get out. In front of him are three doors. The first door leads to a passage through which he exits after $2$ minutes. The second door leads to a tunnel that brings him back to the starting point after $3$ minutes. The third door leads to a tunnel that brings him back to the same place after $5$ minutes. Assuming that each time he chooses any of the three doors with equal probability, determine the expected time for Martin to leave Matej’s MNM room. [/lang]