Quality control: A population of 603 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.

To solve the problems, we first summarize the data provided in the problem:

- Lot A: 87 conforming, 10 nonconforming (Total = 97)
- Lot B: 165 conforming, 40 nonconforming (Total = 205)
- Lot C: 258 conforming, 43 nonconforming (Total = 301)

Total number of wafers = 603 (which matches the total of the three lots).

Let's calculate the required probabilities.

### Part (a)
**What is the probability that the wafer is from Lot C?**

The number of wafers from Lot C is 301.
\[
P(\text{Lot C}) = \frac{\text{Number of wafers from Lot C}}{\text{Total number of wafers}} = \frac{301}{603} \approx 0.4992
\]

### Part (b)
**What is the probability that the wafer is nonconforming?**

To find this, we need to calculate the total number of nonconforming wafers.

Nonconforming wafers:
- Lot A: 10
- Lot B: 40
- Lot C: 43
- Total nonconforming = 10 + 40 + 43 = 93

\[
P(\text{nonconforming}) = \frac{\text{Total nonconforming}}{\text{Total number of wafers}} = \frac{93}{603} \approx 0.1542
\]

### Part (c)
**What is the probability that the wafer is from Lot C and is nonconforming?**

The number of nonconforming wafers from Lot C is 43.

\[
P(\text{Lot C and nonconforming}) = \frac{\text{Nonconforming from Lot C}}{\text{Total number of wafers}} = \frac{43}{603} \approx 0.0713
\]

### Part (d)
**Given that the wafer is from Lot C, what is the probability that it is nonconforming?**

Given that the wafer is from Lot C, we only consider the total wafers in Lot C, which is 301.

\[
P(\text{nonconforming} | \text{Lot C}) = \frac{\text{Nonconforming from Lot C}}{\text{Total wafers from Lot C}} = \frac{43}{301} \approx 0.1432
\]

### Part (e)
**Given that the wafer is nonconforming, what is the probability that it is from Lot C?**

Now we need to find the probability that a nonconforming wafer comes from Lot C.

Using the previous counts:
- Total number of nonconforming wafers = 93.
- Nonconforming wafers from Lot C = 43.

\[
P(\text{Lot C} | \text{nonconforming}) = \frac{\text{Nonconforming from Lot C}}{\text{Total nonconforming}} = \frac{43}{93} \approx 0.4624
\]

### Part (f)
**Are Ev1 and Ev2 independent?**

Two events \(Ev1\) (Lot C) and \(Ev2\) (nonconforming) are independent if:
\[
P(Ev1 \cap Ev2) = P(Ev1) \times P(Ev2)
\]

We found:
- \(P(\text{Lot C}) \approx 0.4992\)
- \(P(\text{nonconforming}) \approx 0.1542\)
- \(P(\text{Lot C and nonconforming}) \approx 0.0713\)

Calculating \(P(\text{Lot C}) \times P(\text{nonconforming})\):
\[
P(\text{Lot C}) \times P(\text{nonconforming}) \approx 0.4992 \times 0.1542 \approx 0.0769
\]

Now we compare it to \(P(\text{Lot C and nonconforming})\):
- \(P(\text{Lot C and nonconforming}) \approx 0.0713\)

Since \(P(\text{Lot C and nonconforming}) \neq P(\text{Lot C}) \times P(\text{nonconforming})\), the events are not independent.

### Summary:
(a) \( \approx 0.4992 \)
(b) \( \approx 0.1542 \)
(c) \( \approx 0.0713 \)
(d) \( \approx 0.1432 \)
(e) \( \approx 0.4624 \)
(f) Not independent.