Answer:
a. 0.4
b. Not independent events
c. 0.47
Step-by-step explanation:
Let A= Practices Gluten free diet
B= Practices Dairy free diet
A and B= Practices Both diets
P(A)=0.20
P(B)=0.15
P(A and B)=0.08
a.
[tex]P(B/A)=\frac{P(A and B)}{P(A)}[/tex]
[tex]P(B/A)=\frac{0.08}{2}[/tex]
[tex]P(B/A)=0.40[/tex]
b.
The two events are independent if P(B/A) =P(B) or P(A/B)=P(A)
As, P(B/A) ≠P(B)
0.4≠0.15
So, the event gluten free diet and dairy free diet are dependent events.
c.
[tex]P(A'/B)=\frac{P(A' and B)}{P(B)}[/tex]
[tex]P(A'and B)= P(B)-P(A and B)[/tex]
[tex]P(A' and B)=0.15-0.08=0.07[/tex]
[tex]P(A'/B)=\frac{P(A' and B)}{P(B)}[/tex]
[tex]P(A'/B)=\frac{0.07}{0.15}[/tex]
[tex]P(A'/B)=0.47[/tex]
