To find the probability of randomly choosing a gel pen, replacing it, and then choosing a fountain pen, we can break it down into two steps:
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Calculating the probability of choosing a gel pen:
- There are 10 gel pens out of a total of 20 pens.
- Probability of choosing a gel pen = \( \frac{10}{20} = \frac{1}{2} \).
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Calculating the probability of choosing a fountain pen after replacing the gel pen:
- There are 4 fountain pens out of a total of 20 pens.
- Probability of choosing a fountain pen = \( \frac{4}{20} = \frac{1}{5} \).
Now, since the events are independent (because we are replacing the gel pen), we multiply the probabilities:
\[ P(\text{Gel pen and then Fountain pen}) = P(\text{Gel pen}) \times P(\text{Fountain pen}) = \frac{1}{2} \times \frac{1}{5} = \frac{1}{10}. \]
Thus, the answer is:
Start Fraction 1 over 10 End Fraction.