To solve the problem, we need to calculate the probability of two independent events: choosing a gel pen and choosing a fountain pen.
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Probability of choosing a gel pen:
- There are 10 gel pens out of a total of 20 pens.
- Probability (gel pen) = \( \frac{10}{20} = \frac{1}{2} \)
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Probability of choosing a fountain pen:
- There are 4 fountain pens out of 20 pens.
- Probability (fountain pen) = \( \frac{4}{20} = \frac{1}{5} \)
Since we are replacing the pen after the first choice, these two events are independent. We can multiply their probabilities:
\[ P(\text{gel pen then fountain pen}) = P(\text{gel pen}) \times P(\text{fountain pen}) = \frac{1}{2} \times \frac{1}{5} = \frac{1}{10} \]
Thus, the probability of randomly choosing a gel pen, replacing it, and then choosing a fountain pen is:
\(\frac{1}{10}\)
The correct response is: Start Fraction 1 over 10 End Fraction