The expected value is $\frac{80}{16}=5$.

If the side facing up is white, and Bert bets on the other side being red, then only one of the three cards would make him win. His chance is therefore $\frac{1}{3}$.

P(3 bets) $={\left(\frac{1}{3}\right)}^3+{\left(\frac{2}{3}\right)}^3=\frac{9}{27}=\frac{1}{3}$.

This cannot happen (after three bets a new series starts and they get new cookies), so the probability is 0.

$\text{P}(T<8.5|\mu =9.2\text{ and }\sigma =0.6)=0.12167$
You would expect $0.12167\cdot 90=10.95$, or $11$ years.

$P(T>10.3|\mu =9.2\text{ and }\sigma =0.6)=0.033376$ for a century, which is about $3$ years per century.

$1-\frac{5}{10}\cdot \frac{4}{9}\cdot \frac{3}{8}\cdot \frac{2}{7}\cdot \frac{1}{6}\approx 0.9960$

$1-\text{P}(V=5|n=5\text{and}p=0.50)=0.96875$

$\text{P}(V<0.25|\mu =0.27\text{ and }\sigma =0.01)\approx 0.0228$

$\text{P}(A\le 2|n=24\text{ and }p=0.0228)\approx 0.9832$

$\text{P}(V<0.25|\mu =m\text{ and }\sigma =0.01)\approx 0.01$ gives you $\frac{(0.25-m)}{0.01}\approx -2.326$ and therefore $m=\mu \approx 0.273$.
On average, the machine needs to dispense $0.273$ litres into each bottle.