Geometry

Question Analysis
This question involves calculating the probability of four independent events that occur during successive die rolls.
The main focus is on correctly determining the favorable outcomes for each roll, calculating their respective probabilities, and then applying the multiplication rule for independent events to find the overall probability.

Key Concept Explanation
Each roll of the die is an independent event, meaning the outcome of one roll does not affect the others.
For multiple independent events, the probability of all events happening together is the product of their individual probabilities, such as .  
When rolling a fair six-sided die, the total number of possible outcomes for each roll is 6, and the probabilities of specific outcomes are determined by the number of favorable outcomes.

Step-by-Step Solution
Calculate the probability of each roll:
For the first roll, the even numbers are 2, 4, 6. So the probability of getting an even number, .
For the second roll, the numbers less than 3 are 1, 2. So the probability of getting a number less than 3, .
For the third roll, the prime numbers are 2, 3, 5. So the probability of getting a prime number,

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