Step 1 :First, calculate the total number of orders from all restaurants. This is done by adding the number of accurate and not accurate orders from all restaurants. In this case, the total number of orders is \(316 + 262 + 247 + 142 + 32 + 53 + 31 + 13 = 1096\).
Step 2 :Next, calculate the total number of orders from Restaurant D. This is done by adding the number of accurate and not accurate orders from Restaurant D. In this case, the total number of orders from Restaurant D is \(142 + 13 = 155\).
Step 3 :Then, calculate the probability of selecting an order from Restaurant D. This is done by dividing the total number of orders from Restaurant D by the total number of orders from all restaurants. In this case, the probability is \(\frac{155}{1096} = 0.14142335766423358\).
Step 4 :Since the selections are made with replacement, the probability of selecting two orders from Restaurant D is the square of the probability of selecting one order from Restaurant D. In this case, the probability is \(0.14142335766423358^2 = 0.020000566093025737\).
Step 5 :Finally, round the final answer to four decimal places. The final answer is \(\boxed{0.0200}\).