The expected value is .
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 .
P(3 bets) .
This cannot happen (after three bets a new series starts and they get new cookies), so the probability is 0.
You would expect , or years.
for a century, which is about years per century.
gives you and therefore .
On average, the machine needs to dispense litres into each bottle.