Marinada '24

[lang=hr] Pošto Mateju sama informacija o idealnom $p$ nije jako korisna, pogotovo jer je vjerojatnost bilo kojeg specifičnog $p$ nula (jer postoji neprebrojivo mnogo mogućih odabira za $p$), odlučio se zapitati koja je vjerojatnost da je $p$ u intervalu $[0.6, 0.7]$. Podsjećamo vas da je Mateju taj $p$ bio nepoznat prije bacanja pa pretpostavlja da je vjerojatnost da je izabran bilo koji $p$ iz intervala $[0, 1]$ jednaka. Zatim su se desila tri bacanja, te su završila s dva pisma i jednom glavom. Odredi, iz Matejeve perspektive, koja je vjerojatnost da je $0.6 \leq p \leq 0.7$. [/lang] [lang=en] Since the information about the ideal $p$ is not very useful to Matej, especially because the probability of any specific $p$ is zero (as there are uncountably many possible choices for $p$), he decided to ask what the probability is that $p$ lies in the interval $[0.6, 0.7]$. We remind you that before the coin tosses, Matej did not know $p$, so he assumes that the probability of choosing any $p$ from the interval $[0, 1]$ is uniform. Then, three coin tosses occurred, resulting in two tails and one head. Determine, from Matej's perspective, the probability that $0.6 \leq p \leq 0.7$. [/lang]