Question

A burrito restaurant used the given table to keep track of the numbers of different types of burritos that were sold and the kinds of beans that people requested.

Consider the following events:
A. The burrito is a chicken burrito.
B. The burrito is a carne asada burrito.
C. The customer requested black beans.
D. The customer requested pinto beans.

Which two events are independent?
A and C
A and D
B and C
B and D

Answer 1

B and D are correct

Explanation:

edge 2020

Answer 2

B and D are independent.

Explanation:

Events A and B are independent when
`P(A\cap B)=P(A)\cdot P(B)`

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

`P(A)=(83)/(240),\ P(B)=(80)/(240)=(1)/(3),\ P(C)=(45)/(240)=(3)/(16),\ P(D)=(72)/(240)=(3)/(10)`

and

`P(A\cap C)=(37)/(240),\ P(A\cap D)=(30)/(240),\ P(B\cap C)=(5)/(240),\ P(B\cap D)=(24)/(240)=(1)/(10)`

Also,

`P(A)\cdot P(C)=(83)/(1280),\ P(A)\cdot P(D)=(83)/(800),\ P(B)\cdot P(C)=(1)/(16),\ P(B)\cdot P(D)=(1)/(10)`

As only
`P(B\cap D)=P(B)\cdot P(D)`, so B and D are independent.