Two problems:

1. Hannah picks two cards from a bowl with 3 orange, 4 purple, and 3 white cards. She does not return them to the bowl after picking them. Find P(the 1st card is not orange and the 2nd card is not white). The first part is simple 7/10 dependent part is not so clear. There are two ways this problem can happen. Choose a purple or a white to satisfy first condition. so you get P(purple)*P(not white) + P(white)*P(not white) leading to the final answer:

7/10*(4/10*6/9+3/10*7/10)

Is that right?

2. What is the probability that you draw a heart from deck of 52 cards don't replace it and then draw an ACE?

13/52* 4/51

Is that right or do I need to account somehow for possibility of an ace of hearts being the first card?