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)

                   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)

Step-by-step 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

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.