Answer: For this, you have 1/3 probability for each day, so if this happens 3 times, the probability will be the product (1/3)*(1/3)*(1/3)= 1/27.
so you have a 3.7% chance of seeing rain the three days.
A way of simulating all the probabilities, is with two D10 (dices with 10 faces)
here if you throw bout dices and get a 0,1,2 or 3 (rounding up) will rain the three days, if you get ani other number, there will be at least one day with no rain.
hope this helped :)