Help understanding and solve these exercises!

#1
Dear friends,
I am studying Biostatistics now and my teacher giving me some exercise. However, it was so difficult for me to understand. Could anyone help me with this?

1)Three independent clinical trials study the efficacy of a new drug vs placebo.
Each trial has a probability of finding that the new drug is better than placebo = 0.8.
a) What is the probability all three trials will show the new drug is better than placebo?
b) What is the probability exactly one trial will show the new drug is better than placebo?
c) What is the probability exactly two trials will show the new drug is better than placebo?
d) If the first trial shows the drug better than placebo what is the probability the next two trials will both show the drug better than placebo?

2.1) For patients with high cholesterol, a decision to start statin, apart from the level of cholesterol itself, it also depends on many factors i.e. 1)the systolic blood pressure, 2)whether the patients have diabetes or not, and 3) whether they are smoking or not. In a cohort study, we found that 40% have their systolic blood pressure within guidelines, 55% have the blood sugar level within guidelines, and 70% don’t smoke. We also find that only 5% of patients have all three measures under control. Do these numbers argue for or against the independence of systolic blood pressure control, diabetes control, and smoking history control?

2.2) For the same cohort of 200 dyslipidemia patients, we find that 70 attend lifestyle-modification classes and 100 attend diet-education classes. If lifestyle-modification classes and diet-education classes are assumed to be independent, then how many patients would you expect to have attended both types of classes?

Thank you for help!
 
#4
for 1a is going to be product of the probability that each of the three trials shows an effect. probably your notes say 'product rule' or something like that.

for 1b, similar, but is going to be one minus product of probability that each trial shows no effect. Your notes say something like 'complement rule'.