part a: No, the outcomes do not seem to be equally likely. There is more of a chance that it will land open end up or open end down then on its side.
part b: The probability for it ending open end up is 50/100. Same with open end down. For on its side, there is 25/100 probability.
part c: In 1000 tosses, I predict the cup will land 250 times on its side.
part d:If we tape a quarter to the bottom of the cup, it will most likely land up end up. This is because the quarter is weighting down the cup, causing it to land upwards.