This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Here's the solution to your probability problem.
Step 1: Interpret the problem statement. The first line is difficult to read, but based on the context of probability problems and the questions asked, we will interpret it as: "A teacher has 8 pens, 3 of which are red." This implies the remaining pens are black. So, we have:
The teacher picks a pen and keeps it, meaning the selections are without replacement.
a) Draw a tree diagram to represent the outcomes.
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Here's the solution to your probability problem. Step 1: Interpret the problem statement.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.