Answer:
B and D are independent.
Step-by-step explanation:
Events A and B are independent when [tex]P(A\cap B)=P(A)\cdot P(B)[/tex]
Here,
A is the event that the burrito is a chicken burrito
B is the event that the burrito is a carne asada burrito
C is the event that the customer requested black beans
D is the event that the customer requested pinto beans
[tex]P(A)=\dfrac{83}{240},\ P(B)=\dfrac{80}{240}=\dfrac{1}{3},\ P(C)=\dfrac{45}{240}=\dfrac{3}{16},\ P(D)=\dfrac{72}{240}=\dfrac{3}{10}[/tex]
and
[tex]P(A\cap C)=\dfrac{37}{240},\ P(A\cap D)=\dfrac{30}{240},\ P(B\cap C)=\dfrac{5}{240},\ P(B\cap D)=\dfrac{24}{240}=\dfrac{1}{10}[/tex]
Also,
[tex]P(A)\cdot P(C)=\dfrac{83}{1280},\ P(A)\cdot P(D)=\dfrac{83}{800},\ P(B)\cdot P(C)=\dfrac{1}{16},\ P(B)\cdot P(D)=\dfrac{1}{10}[/tex]
As only [tex]P(B\cap D)=P(B)\cdot P(D)[/tex], so B and D are independent.
