Geometry

Question Analysis
This question involves calculating the probability of two successive dependent events with specific conditions for each event.
The main challenge lies in correctly identifying the number of favorable outcomes for each event considering the complex categorization of cards, and accurately applying the multiplication rule for dependent events while accounting for the change in the sample space after the first draw.

Key Concept Explanation
Dependent events mean that the outcome of the first card draw affects the probabilities of the second draw.
The multiplication rule for dependent events, , is used to find the combined probability of both events.

Step-by-Step Solution
Calculate the probability of drawing a red card with an even number on the first draw:
Among the 8 red cards, the even - numbered ones are 2, 4, 6, 8. So there are 4 favorable outcomes.
The probability .
Calculate the probability of drawing a blue card with a number greater than 3 on the second draw given that a red card with an even number was drawn on the first draw:
After removing one card, there are 19 cards left. Among the 7 blue cards, the numbers greater than 3 are 4, 5, 6, 7, so there are 4 favorable outcomes.
The probability

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