Question

Complete the two-way frequency table below, which shows the relationship between student gender and how these students travel to school.

Bus (B) Car C) Other (O)Total

Male (M) 350 200 75

Female (F) 300 175 100

Total



What is the P(M|O), and are the events "the student is male" and "the student travels by other" independent events?



A.) they are not independent because P(M ∩ O) ≠ P(M) ⋅ P(O) ,

B.) they are not independent because P(M ∩ O) ≠ P(M) ⋅ P(O) ,

C.) they are independent because P(M ∩ O) = P(M) ⋅ P(O) ,

D.) they are not independent because P(M ∩ O) = P(M) ⋅ P(O)

Answer 1

Bus (B) Car (C) Other (O) Total

Male (M) 350 200 75 625

Female (F) 300 175 100 575

Total 650 375 175 1200

D.) they are not independent because P(M∩O) = P(M|O) ⋅ P(O)

Explanation:

In general: P(A|B) = P(A∩B)/P(B)

For independent variables: P(A|B) = P(A)

P(M|O) = 75/175 = 0.428

P(M) = 625/1200 = 0.521

P(O) = 175/1200 = 0.146

P(M∩O) = 75/1200 = 0.0625