Marinada '21

[lang=hr] Razmnožavanje svake bakterije funkcionira ovako: ili nakon jedne minute ugine, ili se nakon jedne minute pretvori u dvije bakterije. Vjerojatnost da bakterija ugine je $0.24$. Vjerojatnost da se bakterija podijeli u dvije bakterije je $0.76$. Bakterije ugibaju i dijele se nezavisno jedna od druge. Marko na početku ima jednu bakteriju. Koja je vjerojatnost da će mu u nekom trenutku sve bakterije biti mrtve? [/lang] [lang=en] Every bacterium reproduces as follows: either they die after one minute, or they split into two bacteria after one minute. The probability of a bacterium dying is $0.24$. The probability of a bacterium splitting into two bacteria is $0.76$. Bacteria die and split independently of each other. In the beginning, Marko has one bacterium. What's the probability of all his bacteria being dead at some point? [/lang]