To find the probability of randomly choosing a gel pen and then a fountain pen (with replacement), we can calculate this in 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. \[ P(\text{gel pen}) = \frac{10}{20} = \frac{1}{2} \]
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Calculating the probability of choosing a fountain pen:
- There are 4 fountain pens out of a total of 20 pens. \[ P(\text{fountain pen}) = \frac{4}{20} = \frac{1}{5} \]
Since the selections are independent (due to the replacement), we multiply the probabilities of the two events:
\[ P(\text{gel pen and then fountain pen}) = P(\text{gel pen}) \times P(\text{fountain pen}) = \frac{1}{2} \times \frac{1}{5} = \frac{1}{10} \]
Thus, the probability of randomly choosing a gel pen, replacing it, and then choosing a fountain pen is:
\[ \frac{1}{10} \]
The correct answer is:
1/10 (Start Fraction 1 over 10 End Fraction).