The long run proportion of vehicles that pass a certain emissions test is p. Suppose that three vehicles are independently selected for testing. Let X_i = 1 if the ith vehicle passes the test and X_i = 0 otherwise (i = 1, 2, 3), and let T = X₁ + X₂ + X₃. Use the definition of sufficiency to show that T is sufficient for p by obtaining the conditional distribution of the X_i’s given that T = t for each possible value t. Then generalize by giving an analogous argument for the case of n vehicles.