Quality control: A population of 582 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by-whether they conform to a thickness specification, with the results shown in the following table. A wafer is chosen at random from the population. Write your answer as a fraction or a decimal, rounded to four decimal places. \begin{tabular}{ccc} \hline Lot & Conforming & Nonconforming \\ \hline A & 79 & 15 \\ B & 158 & 41 \\ C & 254 & 35 \\ \hline \end{tabular} Send data to Excel (a) What is the probability that the wafer is from Lot C? (b) What is the probability that the wafer is nonconforming? (c) What is the probability that the wafer is from Lot $\mathrm{C}$ and is nonconforming? (d) Given that the wafer is from Lot $C$, what is the probability that it is nonconforming? (e) Given that the wafer is nonconforming, what is the probability that it is from Lot C? (f) Let $E_{1}$ be the event that the wafer comes from Lot C, and let $E_{2}$ be the event that the wafer is nonconforming. Are $E_{1}$ and $E_{2}$ independent?

Step 1 ：Define the number of conforming and nonconforming wafers in each lot as follows: \(\text{lot_A_conforming} = 79\), \(\text{lot_A_nonconforming} = 15\), \(\text{lot_B_conforming} = 158\), \(\text{lot_B_nonconforming} = 41\), \(\text{lot_C_conforming} = 254\), \(\text{lot_C_nonconforming} = 35\)

Step 2 ：Calculate the total number of wafers in each lot by adding the number of conforming and nonconforming wafers: \(\text{lot_A_total} = \text{lot_A_conforming} + \text{lot_A_nonconforming} = 94\), \(\text{lot_B_total} = \text{lot_B_conforming} + \text{lot_B_nonconforming} = 199\), \(\text{lot_C_total} = \text{lot_C_conforming} + \text{lot_C_nonconforming} = 289\)

Step 3 ：Calculate the total number of wafers in the population by adding the total number of wafers in each lot: \(\text{total_wafers} = \text{lot_A_total} + \text{lot_B_total} + \text{lot_C_total} = 582\)

Step 4 ：Calculate the probability that a randomly selected wafer is from Lot C by dividing the total number of wafers in Lot C by the total number of wafers in the population: \(\text{probability_lot_C} = \frac{\text{lot_C_total}}{\text{total_wafers}} = 0.4965635738831615\)

Step 5 ：Final Answer: The probability that a randomly selected wafer is from Lot C is approximately \(\boxed{0.4966}\)