Geometry

Question Analysis
This question involves calculating the probability of two different dependent events occurring in a specific order without replacement.
The main focus is on correctly determining the probabilities of each event considering the changing sample space.

Key Concept Explanation
As with all dependent events, the outcome of the first event impacts the second event.
Here, the removal of the first pen changes the total number of pens and the number of pens of each color available for the second draw.

Step-by-Step Solution
Calculate the probability of drawing a red pen on the first draw: There are 8 pens in total, and 3 are red.
So .
Calculate the probability of drawing a black pen on the second draw given that a red pen was drawn on the first draw: After removing one red pen, there are 7 pens left, and 5 of them are black.
So .
Use the multiplication rule for dependent events:

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