Please help, ty!!

Part A:

 

Let's condense the information we know. I find this small regrouping step helps me immensely.

• There are 65 adults
• There are 15 children
• 41 out of 65 adults ate popcorn
• 6 out of 15 children ate popcorn
• There are 80 people in total

You can even make a quick table, but I think there is not enough information where this is necessary.

 

\(P(\text{Child or Bought Popcorn})=P(\text{Child})+P(\text{Bought Popcorn})-P(\text{Child and Bought Popcorn})\\ P(\text{Child or Bought Popcorn})=\frac{15}{80}+\frac{47}{80}-\frac{6}{80}=\frac{56}{80}=\frac{7}{10}=0.7\)

 

Part B:

 

\(P(\text{Adult or No Popcorn})=P(\text{Adult})+P(\text{No Popcorn})-P(\text{Adult and No Popcorn})\\ P(\text{Adult or No Popcorn})=\frac{65}{80}+\frac{80-(41+6)}{80}-\frac{65-41}{80}\\ P(\text{Adult or No Popcorn})=\frac{65}{80}+\frac{33}{80}-\frac{24}{80}=\frac{74}{80}=0.925 \)