Geometry

Question Analysis
This question involves calculating the probability of a specific combination of four independent events related to password characters.
The main focus is on determining the number of favorable outcomes and total outcomes for each character position and then applying the multiplication rule for independent events to find the overall probability.

Key Concept Explanation
Each character selection in the password is an independent event.
For multiple independent events , , and , the probability of all of them occurring is .
For each position, the probability of a particular character being selected is the ratio of the number of favorable outcomes to the total number of possible outcomes.

Step-by-Step Solution
Calculate the probability for each character position:
For the first character, there is 1 favorable outcome (the digit 5) out of 10 possible digits, so .
For the second character, the even digits are 0, 2, 4, 6, 8, so there are 5 favorable outcomes out of 10, and

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