Volcano X.01192292029

Let's say we divide the $20$ minutes into $20n$ intervals. Then the probability $p$ of any one interval can be found by solving

$1-\left(1-p\right)^{20n}=\dfrac{1}{3}$

$p=1-\left(\dfrac{2}{3}\right)^{\frac{1}{20n}}$

The probability of an eruption over $120n$ intervals, or $2$ hours, is

$1-\left(1-p\right)^{120n}$

$=1-\left(\dfrac{2}{3}\right)^6 \approx 0.9122...$