The outcomes can be characterized as "rain" and "no rain". The probabilities must add to 100% because, collectively, they will describe 100% of the tickets in the box. Therefore the probability for rain is 70% and the probability for no rain is 30%.
[70% * N] = [0.7 * 10] = 7 tickets will have "rain".
[30% * N] = [0.3 * 10] = 3 tickets will have "no rain".
This model is exact, because we did not have to round any values in the computation.
[70% * N] = [0.7 * 5] = [3.5], so we round: [3.5] = 4 tickets will have "rain".
[30% * N] = [0.3 * 5] = [1.5] = 2 tickets will have "no rain".
This model is an approximation, because we had to round. The box contains 4 + 2 = 6 tickets (not 5!) Its probabilities are 4/6 = about 67% for rain and 2/6 = about 33% for no rain.
This box will contain [70% * 20] = 14 tickets with "rain" and [30% * 20] = 6 tickets with "no rain".
This model, like the N=10 model, is exact.
The N=10 and N=20 models are better than the N=5 model because they correctly reproduce the desired probabilities, whereas the N=5 model is just a good approximation. The N=10 model should be considered best because it uses the fewest tickets, but the N=20 model works just fine, too.