Help me please!

(9 marks) (Do this question by hand, showing all your working clearly and stating all used formulas) On any given day Dina will go to the ofce with probability 0.5, work from home with a probability of 0.4 or take the day off with a probability of 0.1. It is also known that if Dina goes to the ofce, she will drink at least 3 cups of coffee with a probability of 0.4. If Dina works from home, she will drink at least 3 cups of coffee with probability 0.6. And if Dina takes the day off, she will drink at least 3 cups of coffee with a probability of 0.2. a) (2 marks) What is the probability that Dina goes to the ofce and drinks less than 3 cups of coffee on any given day? b) (3 marks) What is the probability that Dina drinks at least 3 cups of coffee on any given day? 0) (2 marks) If Dina drinks at least 3 coffees on any given day, what is the probability that she is working at the ofce? d) (2 marks) Is drinking at least 3 cups of coffee on any given day independent of going to the ofce? Explain