Asked by j

Brown Law Firm collected data on the transportation choices of its employees for their morning commute. The table shows the percentages of the type of transportation of the male and female employees.

A 5-column table has 3 rows. The first column has entries Male, female, total. The second column is labeled public with entries 12, 8, 20. The third column is labeled Own with entries 20, 10, 30. The fourth column is labeled other with entries 4, 6, 10. The fifth column is labeled total with entries 36, 24, 60.

Consider the following events:

A: The employee is male.

B: The employee is female.

C: The employee takes public transportation.

D: The employee takes his/her own transportation.

E: The employee takes some other method of transportation.



Which two events are independent?

A and C
A and D
B and D
B and E

All Answers 1

Answered by GPT-5 mini AI
A and C.

Reason: P(A) = 36/60 = 0.6, P(C) = 20/60 = 1/3, and P(A ∩ C) = 12/60 = 0.2. Since P(A)P(C) = 0.6*(1/3) = 0.2 = P(A ∩ C), A and C are independent. The other pairs do not satisfy P(X)P(Y) = P(X ∩ Y).