What is the statistical probability of guessing 4 out of 6 alphanumeric characters correct for a license plate where the first 3 characters must be a letter (a-z) and the last 3 characters must be a number (0-9)?

Step 1 ：First, calculate the total number of possible license plates. There are 26 possible letters for each of the first 3 positions and 10 possible numbers for each of the last 3 positions. So, the total number of possible license plates is \(26^3 * 10^3 = 17,576,000\).

Step 2 ：Next, calculate the number of ways to guess 4 characters correctly. We can guess 4 characters correctly in two ways: either we guess 2 letters and 2 numbers correctly, or we guess 3 letters and 1 number correctly.

Step 3 ：If we guess 2 letters and 2 numbers correctly, there are \(C(3,2)\) ways to choose which 2 letters we guess correctly, and \(C(3,2)\) ways to choose which 2 numbers we guess correctly. For each of these choices, there are 26 possibilities for the incorrect letter and 10 possibilities for the incorrect number. So, the total number of ways to guess 2 letters and 2 numbers correctly is \(C(3,2) * C(3,2) * 26 * 10 = 2,340\).

Step 4 ：If we guess 3 letters and 1 number correctly, there are \(C(3,3)\) ways to choose which 3 letters we guess correctly, and \(C(3,1)\) ways to choose which number we guess correctly. For each of these choices, there are 26 possibilities for the incorrect letter and 10 possibilities for the incorrect number. So, the total number of ways to guess 3 letters and 1 number correctly is \(C(3,3) * C(3,1) * 26 * 10 = 780\).

Step 5 ：So, the total number of ways to guess 4 characters correctly is \(2,340 + 780 = 3,120\).

Step 6 ：The probability of guessing 4 out of 6 characters correctly is the number of ways to guess 4 characters correctly divided by the total number of possible license plates. So, the probability is \(\frac{3,120}{17,576,000} = 0.0001776\), or approximately 0.01776%.

Step 7 ：Finally, check the result. The result is a probability, which should be between 0 and 1, and it is. So, the result meets the requirements of the problem. The final answer is \(\boxed{0.0001776}\).