From the given table, the total number of people, T=269.
1)
The number of adults who like vanila, N=54.
So, P(adult and vanilla) can be found as,
[tex]P\mleft(adult\text{ and vanilla}\mright)=\frac{N}{T}=\frac{54}{269}[/tex]2)
P(chocolate/adult) can be found as,
[tex]P\mleft(chocolate/adult\mright)=\frac{P(\text{choclate and adult)}}{P(\text{adult)}}=\frac{\frac{55}{269}}{\frac{119}{269}}=\frac{55}{269}[/tex]3)
[tex]P\mleft(adult/chocolate\mright)=\frac{P(\text{choclate and adult)}}{P(\text{chocolate)}}=\frac{\frac{55}{269}}{\frac{107}{269}}=\frac{55}{107}[/tex]4)
[tex]P\mleft(notvanilla/teen\mright)=\frac{P(not\text{ vanilla and t}een)}{P(\text{teen)}}=\frac{\frac{12+45}{2}}{\frac{73}{269}}=\frac{57}{73}[/tex]5)
[tex]P\mleft(teen/notvanilla\mright)=\frac{P(\text{teen and not vanilla)}}{P(\text{not vanilla)}}=\frac{\frac{12+45}{269}}{\frac{269-92}{269}}=\frac{57}{177}[/tex]6)
[tex]P\mleft(neither/teenoradult\mright)=\frac{P(\text{neither and teen or adult)}}{P(\text{teen or adult)}}=\frac{\frac{45+10}{269}}{\frac{73+119}{269}}=\frac{55}{192}[/tex]7)
[tex]P\mleft(teenoradult/neither\mright)=\frac{P(\text{teen or adult and neither)}}{P(\text{neither)}}=\frac{\frac{45+10}{269}}{\frac{70}{269}}=\frac{55}{70}=\frac{11}{14}[/tex]
