Your calculations to get 100% are right but you are off for the 50% and. You are only considering one specific outcome. But it doesn't matter if the first question is wrong or the second so the chance is 0.250.75+0.750.25 which is 37.5 or double your answer. We can double check it by looking at it from the other direction.
The chance of failure is 0.75*0.75= 56.25%.
So there is a 43.75% of passing the first go around. Split between a 6.25% to get 100 and 37.5% to get 50.
Same mistake for the second calculations. 44.22% is the chance to get 50%